The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 2 2 2 2 X 1 X 2 2 X X X 1 X X 0 X 1 1 X 1 1 1 1 X 1 1 X X
0 X 0 0 0 0 0 0 0 0 2 X X X+2 0 X+2 X+2 0 2 X X+2 2 X X X 2 X 0 X 2 X+2 X X+2 X+2 X+2 X+2 X 2 0 X+2 X+2 2 X X+2 X 0 2 X 0 2 X X X 0 2 X 0 0 X X+2 X+2 0 0 2 X X+2 0 2 X+2 0 X 0 2 X 2 0 2 0
0 0 X 0 0 0 0 0 0 0 X+2 2 X X X X 0 X X 0 X+2 2 0 X+2 X X X+2 X+2 2 0 X+2 0 2 X+2 X 0 2 2 X 0 2 X X+2 X+2 X X 0 2 X 2 2 0 2 2 X+2 X 2 X 0 2 X X+2 X 2 0 X+2 X+2 2 X+2 2 0 X X 2 2 2 X+2 X
0 0 0 X 0 0 0 X X+2 X X X+2 0 X 2 0 X+2 X+2 2 X+2 X+2 X 0 2 0 2 X X X 2 X 0 X+2 0 X X+2 0 2 X X 2 X+2 0 2 X 0 0 X 2 2 X 2 2 0 0 X 0 2 2 2 X 0 2 X X+2 0 X 2 X X+2 X+2 X+2 2 0 0 X X X
0 0 0 0 X 0 X X X 2 X X X 2 2 X+2 X+2 2 X+2 2 X+2 X X+2 2 2 X 0 X+2 2 X+2 X+2 X X+2 X 0 X+2 X+2 0 0 2 X 2 0 X+2 2 2 X 2 0 X X+2 X X 2 2 X 2 X+2 X 0 X X X+2 X 0 0 2 2 X 0 0 X+2 2 2 2 X+2 X+2 X
0 0 0 0 0 X X 2 X+2 X+2 X X X+2 0 X 2 2 2 X X+2 0 2 2 0 X 0 X 2 2 X+2 X+2 X+2 X+2 0 2 2 2 2 0 0 X+2 X+2 X+2 X+2 X X 2 X 2 X X 0 2 X+2 0 X+2 X 2 X+2 X X 0 0 X X X 0 0 0 X X+2 0 X X+2 0 X+2 X+2 X+2
0 0 0 0 0 0 2 2 2 2 2 2 2 0 2 0 0 0 2 2 0 0 0 0 2 2 0 2 2 0 0 0 0 2 2 2 2 2 2 0 2 0 0 0 2 0 2 2 2 0 0 2 0 2 2 2 0 2 0 2 0 0 2 2 0 0 0 2 0 0 0 0 2 2 0 0 0 0
generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.
Homogenous weight enumerator: w(x)=1x^0+76x^66+146x^67+237x^68+302x^69+355x^70+504x^71+549x^72+692x^73+995x^74+1128x^75+1137x^76+1362x^77+1457x^78+1404x^79+1293x^80+1062x^81+929x^82+708x^83+532x^84+434x^85+298x^86+198x^87+172x^88+140x^89+98x^90+66x^91+40x^92+38x^93+14x^94+6x^95+4x^96+2x^97+2x^98+2x^100+1x^112
The gray image is a code over GF(2) with n=312, k=14 and d=132.
This code was found by Heurico 1.16 in 26.5 seconds.