The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  X  0  X  X X^2  0 X^2  1  0 X^2  1  X  0  1  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X  0 X^2 X^2 X^2+X  0  X X^2  X  X X^2  X X^2 X^2 X^2+X  0  X X^2  X  0
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X  0 X^2 X^2 X^2  X X^2  X  0  X  X X^2  X  X  X  X X^2+X X^2  0  0
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2  X X^2  0  0 X^2+X X^2  X X^2+X X^2+X  X X^2  X  0 X^2+X  X X^2+X X^2  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 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 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 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+23x^28+72x^29+98x^30+204x^31+255x^32+302x^33+407x^34+458x^35+516x^36+448x^37+402x^38+302x^39+198x^40+184x^41+96x^42+54x^43+29x^44+16x^45+20x^46+6x^47+2x^48+2x^49+1x^50

The gray image is a linear code over GF(2) with n=144, k=12 and d=56.
This code was found by Heurico 1.16 in 0.531 seconds.