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 X^3+X^2 X^3+X^2  X  1 X^3 X^2  X  X  X
 0  X  0  X X^3  0 X^3+X  X X^2 X^2+X X^2 X^2+X X^3+X^2 X^2 X^3+X^2+X X^2+X  0 X^3  X X^3+X X^2  0 X^3+X^2+X  X X^3 X^3+X^2+X X^3+X^2  X  X X^3  0 X^3+X^2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^3+X^2+X  X X^3  0 X^2+X X^3+X X^3+X^2 X^3 X^3+X^2+X X^3+X  0 X^3 X^3+X X^2+X X^3+X^2+X  X X^2 X^2 X^2 X^3+X^2 X^3+X^2+X X^2+X X^3+X^2

generates a code of length 32 over Z2[X]/(X^4) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+104x^29+129x^30+206x^31+192x^32+184x^33+84x^34+72x^35+38x^36+8x^37+3x^38+2x^39+1x^48

The gray image is a linear code over GF(2) with n=256, k=10 and d=116.
This code was found by Heurico 1.16 in 0.015 seconds.