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.