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 X 1 1 1 1 0 1 X 1 1 X 1 1 2 1 1 1 1 1 2 X 2 1 1 1 1 1 X 1 2 1 2 1 1 X 1
0 X 0 0 0 0 0 2 2 X X+2 X X X X+2 X 0 X+2 2 X 2 X 0 X 2 X+2 X 0 X+2 2 X+2 0 0 2 0 X X X+2 X X X X+2 X 2 X+2 X+2 X X+2 X+2 X 2 0 0 X+2 0 2 X 0 X+2 2 X X+2 2 0 X+2 0 X X 0 X 0 2 2 2
0 0 X 0 0 2 X+2 X X X X X X+2 0 0 0 2 2 X+2 X 2 0 0 X+2 2 2 X X+2 0 X X X+2 X X+2 X+2 0 2 0 X+2 X 2 X+2 X X X X+2 X+2 X+2 0 2 0 0 0 2 X+2 X X 2 2 X 2 0 0 X X X+2 2 2 0 0 2 X X+2 2
0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 0 X X 2 X 2 X+2 0 X+2 0 2 X 2 X X 2 X X 0 0 2 X 0 X+2 2 X+2 X 0 X+2 X 2 0 2 X+2 X X+2 0 0 0 X 2 X X+2 X+2 X+2 X X X 2 X+2 X+2 0 2 X+2 X 2 2 2 0 0 X+2 0
0 0 0 0 X X 2 X+2 X X+2 2 2 X 2 X+2 X X 2 2 X+2 0 X+2 0 X+2 X+2 X+2 0 X+2 0 X 0 2 0 X+2 X 0 2 X+2 X 0 X+2 X X 2 2 2 0 0 2 X X X+2 2 0 X 0 0 0 X X+2 X 0 X 2 0 X+2 0 0 X+2 X 2 0 2 0
generates a code of length 74 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.
Homogenous weight enumerator: w(x)=1x^0+23x^66+62x^67+74x^68+98x^69+235x^70+72x^71+231x^72+56x^73+438x^74+54x^75+248x^76+40x^77+192x^78+42x^79+34x^80+46x^81+25x^82+14x^83+17x^84+10x^85+13x^86+10x^87+2x^88+6x^89+2x^90+2x^91+1x^124
The gray image is a code over GF(2) with n=296, k=11 and d=132.
This code was found by Heurico 1.16 in 0.52 seconds.