The generator matrix
1 0 1 1 1 X^2 1 1 0 1 1 0 X 1 1 1 1 0 1 1 1 1 X^2 X^2 X 0 X^2+X 0 X^2+X X^2+X X X
0 1 1 0 X+1 1 1 0 1 X^2 X+1 1 1 X^2+1 X^2+X X X+1 1 X X X^2+X+1 1 1 1 1 0 1 1 1 1 1 1
0 0 X 0 0 X^2 0 X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2 0 X^2 0 X^2 X^2+X X X^2+X X^2+X X X^2+X 0 X X^2 X^2 0 0 X X
0 0 0 X X^2 X X^2+X X^2+X X^2+X X^2 X X^2 X^2+X X^2 0 X X^2+X 0 X^2 X^2+X 0 X X^2 X^2+X X 0 X X X^2+X 0 0 X^2
generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+38x^28+128x^29+216x^30+152x^31+51x^32+112x^33+152x^34+96x^35+32x^36+16x^37+12x^38+8x^39+4x^40+2x^44+4x^46
The gray image is a linear code over GF(2) with n=128, k=10 and d=56.
This code was found by Heurico 1.16 in 0.0313 seconds.