The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 0 1 X^2 1 X 1 1 X 1 X X 1
0 X 0 0 0 X X^2+X X X^2 X^2 0 0 X X X X^2+X 0 0 X X^2+X X^2 X^2 X^2 X^2+X X^2+X 0 X^2 0 X X^2+X X^2 0
0 0 X 0 X X X 0 X^2 0 X X^2+X X^2+X 0 X^2+X 0 X^2 X^2+X 0 X X^2 X X X^2 0 X^2+X X X X 0 X^2 0
0 0 0 X X 0 X X^2+X 0 X X X^2 X^2 X^2+X X 0 X^2 X X X^2+X X X^2+X X X^2 X 0 0 X X^2+X X^2 X^2+X 0
0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0
0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2
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+84x^26+8x^27+220x^28+72x^29+304x^30+176x^31+368x^32+176x^33+284x^34+72x^35+148x^36+8x^37+88x^38+30x^40+8x^42+1x^48
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 0.137 seconds.