The generator matrix

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

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+96x^29+49x^30+176x^31+412x^32+160x^33+46x^34+64x^35+2x^36+1x^38+16x^39+1x^56

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 0.032 seconds.