The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 0 X 0 X^2 1 X^2 X^2 1 X^2 X 1 1 1
0 X 0 0 0 0 0 X^2 X^2 X X^2+X X X^2 X^2+X X^2+X X X^2+X 0 X X X 0 X X 0 X^2 X^2+X X 0 X^2 X X
0 0 X 0 0 X^2 X^2+X X X X X X X^2+X X^2 X^2+X X^2 X^2 X X X X^2 X X X^2+X X 0 X X X^2 X^2+X X^2+X X^2+X
0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 X X^2+X 0 X^2+X X^2 0 X^2 X X^2+X X^2+X X X^2+X X^2 X 0 X^2 0 0 X^2+X 0
0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X^2 0 X X 0 X X X^2 0 X^2 X^2 X 0 X X^2 0 X^2 X X^2 X^2 X^2+X
generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.
Homogenous weight enumerator: w(x)=1x^0+36x^26+86x^27+166x^28+198x^29+197x^30+254x^31+260x^32+234x^33+193x^34+150x^35+93x^36+74x^37+47x^38+18x^39+23x^40+6x^41+7x^42+4x^43+1x^44
The gray image is a linear code over GF(2) with n=128, k=11 and d=52.
This code was found by Heurico 1.16 in 0.127 seconds.