The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^3  1  1  0  X  1  1 X^3 X^2  1  1  1  1  X  X
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^3  0 X^2+X X^3+X X^2+X  X X^3+X^2 X^3+X^2 X^2+X  X  0 X^3+X  X  X X^3 X^3+X^2+X  X  X  0  0 X^3+X^2+X  X X^2+X X^2+X
 0  0 X^3+X^2  0 X^2  0 X^3  0  0 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3  0 X^3 X^2 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2  0 X^3 X^2 X^2  0 X^3
 0  0  0 X^3+X^2  0 X^3 X^3 X^2 X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3+X^2 X^2 X^2 X^3+X^2  0  0 X^2  0 X^3 X^3+X^2  0  0 X^3  0 X^3
 0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  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+346x^28+64x^29+608x^30+448x^31+1190x^32+448x^33+608x^34+64x^35+290x^36+24x^40+4x^44+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 105 seconds.