The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+296x^76+198x^77+579x^78+192x^79+586x^80+200x^81+486x^82+152x^83+426x^84+100x^85+285x^86+84x^87+203x^88+38x^89+76x^90+32x^91+72x^92+18x^93+38x^94+4x^95+16x^96+6x^97+8x^98

The gray image is a linear code over GF(2) with n=328, k=12 and d=152.
This code was found by Heurico 1.16 in 1.08 seconds.