The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+43x^74+172x^75+191x^76+250x^77+314x^78+354x^79+321x^80+318x^81+306x^82+328x^83+298x^84+332x^85+261x^86+182x^87+196x^88+46x^89+79x^90+26x^91+10x^92+8x^93+13x^94+24x^95+2x^96+4x^97+4x^98+2x^99+4x^100+2x^101+3x^102+1x^108+1x^110

The gray image is a linear code over GF(2) with n=328, k=12 and d=148.
This code was found by Heurico 1.16 in 1.45 seconds.