The generator matrix

 1  0  0  0  1  1  1  1 X^2  1 X^2+X  X  1 X^2  1  1  1  X  0  1  X  1  0  1  1 X^2+X X^2+X X^2+X X^2 X^2  1  1
 0  1  0  0  0  1 X^2 X^2+1  1 X^2+X+1 X^2  1  0  1 X^2+1 X^2 X+1  1 X^2+X  X  1 X^2+X+1 X^2 X^2+X X^2+X X^2  1  X  1  0 X+1 X^2+X+1
 0  0  1  0  0  1 X^2+1 X^2+X X+1 X^2+1  1 X^2 X^2+X+1 X^2+1  X  X X^2 X^2+X+1  X  X  0 X+1  1  1 X^2+X+1  0  1  1 X^2+1  1  X  1
 0  0  0  1  1 X^2  1 X+1 X+1 X^2+1 X^2+1 X^2+1  X  X  0 X^2+1 X^2 X+1  1 X^2  1 X+1 X^2+X+1 X^2  1  1  X X^2 X^2+X X^2+1 X^2+X+1  X
 0  0  0  0  X  0  0  0  0  X  X  X X^2+X  X  X X^2+X X^2 X^2  X X^2+X X^2  0 X^2 X^2 X^2 X^2+X X^2 X^2+X X^2 X^2+X  X 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+312x^26+532x^27+1211x^28+1200x^29+1872x^30+1904x^31+2288x^32+1768x^33+2218x^34+1300x^35+997x^36+384x^37+252x^38+72x^39+47x^40+8x^41+18x^42

The gray image is a linear code over GF(2) with n=128, k=14 and d=52.
This code was found by Heurico 1.13 in 205 seconds.