The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  X  X  1 X^2  X  1  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  0 X^2 X^3+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+X^2 X^3+X^2 X^3 X^3 X^3+X^2
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2  0 X^3 X^2 X^3 X^3+X^2  0 X^3+X^2 X^2 X^3 X^3 X^2 X^3 X^2 X^3  0 X^3 X^2  0 X^2  0 X^3
 0  0  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3
 0  0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3
 0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0  0 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+185x^28+48x^29+464x^31+679x^32+464x^33+48x^35+131x^36+24x^40+3x^44+1x^52

The gray image is a linear code over GF(2) with n=256, k=11 and d=112.
This code was found by Heurico 1.16 in 7.03 seconds.