The generator matrix

 1  0  0  0  1  1  1  0  0 X^2 X^2  1  1  1  1  1 X^2+X X^2+X  1  1  1  X X^2  1  1  1  1  0  0 X^2+X  1 X^2 X^2  1 X^2+X  1  1  X  0 X^2  1  X X^2+X  0  1  1  1  1  0  1  1 X^2+X  1 X^2 X^2+X  1  1  1  X  1  X  X  1  1  0  X X^2+X  1  0  1  1 X^2  X  1  1  1  0  X  1  1  1  1
 0  1  0  0  0  1  1  1 X^2  1  1  0  1  1  0  X  X  1 X^2+1 X^2+X X^2  1 X^2  0 X^2+X+1 X+1 X+1  1  1 X^2  X  1  X X^2+X+1  1 X^2+X  0  1  1  0 X^2+X+1  X X^2  1  X X^2 X^2 X^2+X+1  1  X X^2+1  1 X^2+X  X  1  1  X X+1  1 X+1 X^2  1 X^2+X X^2+X+1  1  1  1 X^2+X+1 X^2+X X^2+1  1  X  1  1 X+1 X+1  1 X^2 X^2+1 X^2 X^2 X^2+X
 0  0  1  0  1 X^2 X^2+1  1  1  0  1 X^2  1  0 X^2+1 X^2  1  X X^2+X X^2+1  X  1  X X^2+X+1 X^2+1  0 X^2+1  X X^2+X+1  1 X^2+X  X  1 X^2+X  0 X^2+1 X+1 X+1 X^2  1 X^2+1  1 X^2  X X+1 X^2+X+1 X^2+1  X X^2+1 X^2 X^2+X+1 X+1  1  1  0  1  1  X X^2+X+1 X^2+X+1  1 X^2+1  X X^2+X+1 X^2+X+1  0  1  X  1 X^2  X X^2  0  0  1 X^2+1 X^2+1  1  1 X^2+X  0  0
 0  0  0  1 X^2  0 X^2 X^2  1  1 X^2+1  1  1 X^2+1 X^2+1 X^2+X X+1 X^2  0  0 X+1  X  1 X+1 X^2+X X^2+X+1  1  1 X+1 X^2+X  X X^2+X+1  0  1  0  X X^2+1  0 X^2+X+1 X^2+X+1 X^2  0  1  X X^2  0 X^2+X+1  0 X^2+X X+1  X X^2+X X^2+1 X^2+X X+1 X+1  X X+1 X^2+X+1 X^2 X+1 X^2+X X^2 X^2+X+1 X^2+X X^2+X X^2+1  X X^2+X+1 X^2+X+1  0  1 X^2+1  X X^2+X+1 X^2  0  1 X+1 X^2  X 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+244x^76+276x^77+520x^78+316x^79+479x^80+312x^81+394x^82+204x^83+306x^84+144x^85+236x^86+108x^87+186x^88+108x^89+66x^90+36x^91+86x^92+20x^93+32x^94+8x^95+10x^96+4x^97

The gray image is a linear code over GF(2) with n=328, k=12 and d=152.
This code was found by Heurico 1.11 in 0.484 seconds.