The generator matrix

 1  0  0  0  1  1  1  X  0  1  1 X^2  1  X  1  1  1  X  1  1  0  1  1  1  1  1  1  X  X  1  1  1
 0  1  0  0  1 X^2 X+1  1  X  1  0  1 X+1  1  0 X^2+X+1 X^2  1 X^2+X X^2+1  1  1  X X^2+X X^2 X+1 X^2+X+1 X^2+X  1  1 X^2+X+1  1
 0  0  1  0  1 X^2+1 X^2 X^2+1  1 X+1 X^2+X+1  1  X X^2 X^2  1 X^2+X  1 X^2+1  X  X  0  0 X^2+X+1 X+1 X^2+X+1  X  0  0  X X^2+X+1 X^2
 0  0  0  1 X^2  1 X^2+1 X^2+X+1 X+1  1 X^2+X X^2+X X^2  1 X^2+X+1 X+1 X^2+X+1 X^2+1 X^2+1  X X+1 X^2+1 X^2+X  0 X^2+1 X+1 X+1  1 X^2  0  1  1

generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+148x^27+264x^28+470x^29+493x^30+486x^31+490x^32+496x^33+383x^34+406x^35+222x^36+146x^37+59x^38+14x^39+7x^40+8x^41+1x^42+2x^43

The gray image is a linear code over GF(2) with n=128, k=12 and d=54.
This code was found by Heurico 1.11 in 0.109 seconds.