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

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+394x^30+32x^31+690x^32+264x^33+1090x^34+672x^35+1455x^36+816x^37+1172x^38+256x^39+643x^40+8x^41+346x^42+151x^44+38x^46+2x^48+1x^60

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 2.46 seconds.