The generator matrix

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

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+266x^28+88x^29+782x^30+408x^31+1140x^32+456x^33+516x^34+72x^35+306x^36+46x^38+14x^40+1x^48

The gray image is a linear code over GF(2) with n=256, k=12 and d=112.
This code was found by Heurico 1.16 in 3.83 seconds.