The generator matrix

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

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+592x^28+1000x^29+2376x^30+2624x^31+3403x^32+2576x^33+2234x^34+896x^35+522x^36+72x^37+60x^38+24x^40+2x^42+2x^44

The gray image is a linear code over GF(2) with n=256, k=14 and d=112.
This code was found by Heurico 1.16 in 450 seconds.