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  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1
 0  X  0  0  0  X X^2+X X^2+X X^2  0  0  0  X  X X^2+X X^2+X X^2 X^2  X  X X^2  0  X X^2+X X^2 X^2 X^2+X X^2+X  0 X^2+X X^2+X  0 X^2+X  0 X^2 X^2+X X^2+X X^2  0  X X^2 X^2+X  0  X X^2+X X^2  X  0  0 X^2  X X^2+X X^2  0 X^2  X  X  0  X  X X^2  X  0  0 X^2  0  0 X^2+X X^2 X^2+X  0 X^2 X^2+X X^2+X  X X^2+X X^2  0  0 X^2  X X^2
 0  0  X  0  X  X  X X^2  0  0  X X^2+X  X  0 X^2+X  0 X^2 X^2+X X^2 X^2 X^2+X X^2  X  X X^2 X^2  0  X X^2+X  X X^2 X^2+X X^2+X  X  X  0  0 X^2 X^2  X X^2+X X^2  X X^2+X X^2 X^2 X^2+X  0 X^2  0 X^2+X X^2+X  0  0 X^2+X X^2  X X^2+X X^2 X^2  X X^2 X^2+X  0  0 X^2+X  X X^2+X X^2  X X^2+X X^2+X  X  0  0 X^2 X^2 X^2 X^2+X  0 X^2+X  0
 0  0  0  X  X  0  X  X  X  0 X^2+X X^2  0 X^2+X X^2+X X^2  X X^2+X X^2+X  0 X^2 X^2 X^2 X^2+X X^2+X X^2 X^2+X  0  0 X^2+X X^2 X^2+X  0 X^2+X X^2  0 X^2+X  0  X X^2+X  0 X^2  X  0  X X^2  X X^2+X  0  X X^2 X^2+X  0 X^2+X  X  X X^2 X^2 X^2+X  0 X^2 X^2 X^2+X  X  X  0 X^2  X  0 X^2  X X^2+X X^2  X X^2+X X^2+X X^2+X  0  0  0 X^2+X X^2+X
 0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 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+49x^76+101x^78+112x^80+128x^81+260x^82+128x^83+119x^84+61x^86+36x^88+26x^90+2x^92+1x^160

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 0.472 seconds.