The generator matrix

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

generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+19x^28+70x^29+68x^30+56x^31+88x^32+94x^33+56x^34+8x^35+17x^36+26x^37+4x^38+2x^40+2x^41+1x^56

The gray image is a linear code over GF(2) with n=128, k=9 and d=56.
This code was found by Heurico 1.16 in 0.0168 seconds.