The generator matrix

 1  0  0  0  1  1  1  X X^2+X  1  1  0  1 X^2  1  1  1  X  1  1  1 X^2 X^2+X  1  1  1 X^2  1 X^2+X  1  1  1
 0  1  0  0 X^2  1 X^2+1  1  1  X X^2+X  1 X+1 X^2+X X+1  X  0  0 X^2 X^2+X+1 X^2+X+1 X^2  1 X^2+X  X  1  1 X^2  1 X^2  X  X
 0  0  1  0 X^2+1  1 X^2 X^2+X+1  1  0 X+1  X X^2+1  1  X X^2+X X+1  1 X^2+X+1 X^2  0  1  X X^2  1 X+1 X^2+X  1 X^2+X+1 X^2+X X^2 X^2+X
 0  0  0  1  1 X^2 X^2+X+1 X^2+X+1  X  1 X^2 X^2+1 X+1 X^2+1  X  1 X+1 X+1 X^2+X  X X^2+X+1 X^2+X X+1 X^2+X X^2+X  0 X^2+X+1 X+1 X^2+X+1 X^2  0 X^2+X+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+100x^27+353x^28+440x^29+467x^30+518x^31+453x^32+474x^33+476x^34+392x^35+205x^36+100x^37+75x^38+14x^39+12x^40+10x^41+6x^42

The gray image is a linear code over GF(2) with n=128, k=12 and d=54.
This code was found by Heurico 1.16 in 0.259 seconds.