The generator matrix

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

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+268x^30+128x^31+342x^32+32x^33+172x^34+32x^35+39x^36+8x^38+1x^40+1x^44

The gray image is a linear code over GF(2) with n=256, k=10 and d=120.
This code was found by Heurico 1.16 in 18.5 seconds.