The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+166x^28+32x^29+256x^30+160x^31+807x^32+320x^33+640x^34+320x^35+792x^36+160x^37+256x^38+32x^39+128x^40+18x^44+8x^48

The gray image is a linear code over GF(2) with n=136, k=12 and d=56.
This code was found by Heurico 1.16 in 93.2 seconds.