The generator matrix

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

generates a code of length 32 over Z2[X]/(X^4) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+14x^30+288x^31+31x^32+96x^33+16x^34+64x^35+2x^46

The gray image is a linear code over GF(2) with n=256, k=9 and d=120.
This code was found by Heurico 1.16 in -3.24e-008 seconds.