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 X^2  1  1  1  1  1 X^2  X X^2  1  1  1  1  1  X  1 X^2  1 X^2  1  1  X  1
 0  X  0  0  0  0  0 X^2 X^2  X X^2+X  X  X  X X^2+X  X  0 X^2+X X^2  X X^2  X  0  X X^2 X^2+X  X  0 X^2+X X^2 X^2+X  0  0 X^2  0  X  X X^2+X  X  X  X X^2+X  X X^2 X^2+X X^2+X  X X^2+X X^2+X  X X^2  0  0 X^2+X  0 X^2  X  0 X^2+X X^2  X X^2+X X^2  0 X^2+X  0  X  X  0  X  0 X^2 X^2 X^2
 0  0  X  0  0 X^2 X^2+X  X  X  X  X  X X^2+X  0  0  0 X^2 X^2 X^2+X  X X^2  0  0 X^2+X X^2 X^2  X X^2+X  0  X  X X^2+X  X X^2+X X^2+X  0 X^2  0 X^2+X  X X^2 X^2+X  X  X  X X^2+X X^2+X X^2+X  0 X^2  0  0  0 X^2 X^2+X  X  X X^2 X^2  X X^2  0  0  X  X X^2+X X^2 X^2  0  0 X^2  X X^2+X X^2
 0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  0  X  X X^2  X X^2 X^2+X  0 X^2+X  0 X^2  X X^2  X  X X^2  X  X  0  0 X^2  X  0 X^2+X X^2 X^2+X  X  0 X^2+X  X X^2  0 X^2 X^2+X  X X^2+X  0  0  0  X X^2  X X^2+X X^2+X X^2+X  X  X  X X^2 X^2+X X^2+X  0 X^2 X^2+X  X X^2 X^2 X^2  0  0 X^2+X  0
 0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2 X^2  X X^2 X^2+X  X  X X^2 X^2 X^2+X  0 X^2+X  0 X^2+X X^2+X X^2+X  0 X^2+X  0  X  0 X^2  0 X^2+X  X  0 X^2 X^2+X  X  0 X^2+X  X  X X^2 X^2 X^2  0  0 X^2  X  X X^2+X X^2  0  X  0  0  0  X X^2+X  X  0  X X^2  0 X^2+X  0  0 X^2+X  X X^2  0 X^2  0

generates a code of length 74 over Z2[X]/(X^3) 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 linear code over GF(2) with n=296, k=11 and d=132.
This code was found by Heurico 1.16 in 0.519 seconds.