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

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+72x^76+78x^78+32x^79+127x^80+96x^81+302x^82+96x^83+54x^84+32x^85+26x^86+47x^88+42x^90+18x^92+1x^152

The gray image is a linear code over GF(2) with n=328, k=10 and d=152.
This code was found by Heurico 1.16 in 0.495 seconds.