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

generates a code of length 36 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+161x^28+386x^30+56x^31+761x^32+288x^33+1020x^34+664x^35+1507x^36+704x^37+1056x^38+296x^39+724x^40+32x^41+324x^42+8x^43+155x^44+30x^46+18x^48+1x^52

The gray image is a linear code over GF(2) with n=144, k=13 and d=56.
This code was found by Heurico 1.16 in 2.34 seconds.