The generator matrix

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

generates a code of length 32 over Z2[X]/(X^4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+42x^28+153x^30+128x^31+408x^32+128x^33+122x^34+16x^36+13x^38+12x^40+1x^56

The gray image is a linear code over GF(2) with n=256, k=10 and d=112.
This code was found by Heurico 1.16 in 0.032 seconds.