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 X 1 1 1 1 1 1 1 1 1 0 1 1 1 2 1 1 0 1 X 1 0 1 1 1 1 2 1 2 2 X X 2 2 1 1 0 X 1
0 X 0 0 0 2 0 2 0 X+2 X X+2 X X X X 0 0 2 2 X+2 X X+2 X 2 X X+2 X+2 0 2 X 2 2 2 0 0 X+2 0 2 X 0 X+2 2 0 0 X+2 2 2 X X X 0 X+2 X X+2 0 X+2 2 0 2 X+2 X X X 2 X X+2 2 2 0 X X+2 X X+2 X
0 0 X 0 0 2 X X X+2 X X 2 X X+2 2 2 0 2 X X X+2 X+2 0 2 0 X 0 0 X X+2 X+2 0 0 0 X X+2 X+2 X X X+2 0 X+2 2 X+2 X+2 X 2 2 2 0 2 2 0 X+2 X+2 0 0 X X+2 0 0 X+2 2 0 X X+2 X 2 X X X 0 X+2 2 2
0 0 0 X 0 X X X+2 2 2 2 2 X X X+2 X 0 X+2 X 0 2 X+2 X+2 0 X+2 X+2 2 X X+2 2 2 2 2 2 0 2 0 X X X+2 X+2 2 X+2 X X+2 X+2 X 0 X 2 0 0 2 2 X 2 0 X+2 0 X X X+2 0 2 0 X+2 X X 2 2 X X+2 X 0 X+2
0 0 0 0 X X 2 X X+2 X+2 2 X+2 X 0 0 X+2 2 X X 2 2 X+2 X 0 2 0 X 0 0 X+2 X X+2 0 X X 2 X+2 X 0 2 2 0 X+2 X 0 X+2 0 X 0 X X 0 2 X+2 X+2 X X 2 X+2 X+2 X+2 X X+2 2 X+2 2 0 X X X 0 2 X+2 2 0
generates a code of length 75 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.
Homogenous weight enumerator: w(x)=1x^0+132x^68+16x^69+232x^70+64x^71+222x^72+92x^73+246x^74+148x^75+235x^76+136x^77+146x^78+40x^79+138x^80+12x^81+74x^82+4x^83+59x^84+30x^86+10x^88+8x^90+2x^92+1x^120
The gray image is a code over GF(2) with n=300, k=11 and d=136.
This code was found by Heurico 1.16 in 0.57 seconds.