The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  X  X  X  X  0  1  1  1  1  1  1  1  1  0 X^2  1  1
 0  X  0  X  0  0  X X^2+X  0 X^2 X^2+X  X  0  X  X X^2  0  0 X^2 X^2+X  X  X  X X^2 X^2 X^2  0  X X^2 X^2+X X^2  0  0  X  X  0
 0  0  X  X  0 X^2+X  X  0 X^2  X  0  X  0 X^2+X X^2  X X^2+X  X  X  0  X  X  0  X  X  X X^2+X  X X^2+X X^2  0  0  X X^2+X X^2 X^2
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  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+30x^28+52x^29+108x^30+182x^31+208x^32+336x^33+416x^34+468x^35+562x^36+464x^37+400x^38+312x^39+178x^40+160x^41+80x^42+60x^43+38x^44+12x^45+20x^46+2x^47+5x^48+2x^52

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 0.545 seconds.