The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  0  1  1  1 X^2  1  X X^2+X  1  1  1  1  X  X  1  1  X  X  1  1  0
 0  1  1  0  1  1  X X^2+X+1  1 X^2+X  1 X^2+X+1  0  1 X+1 X^2+1 X^2  1  0  1  1 X+1 X^2  1  X  1  1 X^2+X+1  X  X X^2+X  X X^2+X  1
 0  0  X  0  0  0  0  0  0 X^2 X^2  X  X  X  0 X^2+X  X X^2+X X^2+X X^2+X X^2 X^2+X  0 X^2 X^2+X X^2+X  X X^2+X X^2  0  X X^2 X^2+X X^2+X
 0  0  0  X  0  0  X X^2  X X^2 X^2+X  0  0  0 X^2+X X^2+X X^2+X X^2+X  X X^2  X  0 X^2  X X^2 X^2+X  X X^2 X^2+X X^2+X  X X^2 X^2 X^2
 0  0  0  0  X  0  0  X X^2 X^2  0 X^2 X^2+X  X X^2+X X^2 X^2+X  X  0 X^2 X^2+X X^2+X X^2+X X^2  0 X^2  0  X  X X^2+X  X X^2  X X^2+X
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  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 27.

Homogenous weight enumerator: w(x)=1x^0+72x^27+169x^28+310x^29+452x^30+626x^31+939x^32+1036x^33+993x^34+1078x^35+960x^36+620x^37+403x^38+254x^39+128x^40+76x^41+39x^42+18x^43+11x^44+6x^45+1x^46

The gray image is a linear code over GF(2) with n=136, k=13 and d=54.
This code was found by Heurico 1.16 in 8.03 seconds.