The generator matrix

 1  0  0  0  1  1  1  1 X^2 X^2+X  1  1 X^2+X  1  0  0  1 X^2+X  1  1  X X^2  X  1  1  0  0  1  0  1  X  1 X^2  1  1  1
 0  1  0  0  0  1 X^2+X+1  1  1  1  X X^2 X^2 X^2+X+1  1  X X^2+1  1  X  0  1 X^2+X  1 X+1  1 X^2  0  0  1 X^2+X  X X^2+X+1  1 X^2+1  0  0
 0  0  1  0  1  1  X  0  1 X^2+X+1 X^2+X+1  X  1 X^2+X+1  0 X^2 X^2+1 X^2+X  0 X^2  0  1  1 X^2+X  0  1  X X^2 X^2+X X^2+X+1  1  1 X+1 X^2+X X^2  0
 0  0  0  1  1  0 X^2  1 X+1 X^2 X^2  1 X^2+X+1 X^2+X+1 X^2+1  1  X  0 X^2+X X^2+X+1  1 X^2 X^2+X+1 X^2+1  X  1  1 X^2  1 X^2+X+1  X  X X^2+X X+1  X  0
 0  0  0  0  X  0  0 X^2 X^2 X^2  X  0 X^2 X^2+X X^2+X X^2+X  X  X  0  0 X^2+X  0  0 X^2+X X^2 X^2  0 X^2+X  X X^2 X^2+X X^2  X X^2+X X^2  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0  0  0 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+56x^28+300x^29+686x^30+1312x^31+1857x^32+2714x^33+2954x^34+4330x^35+4081x^36+4426x^37+3347x^38+2862x^39+1707x^40+1118x^41+525x^42+294x^43+103x^44+50x^45+39x^46+2x^47+3x^48+1x^50

The gray image is a linear code over GF(2) with n=144, k=15 and d=56.
This code was found by Heurico 1.16 in 18 seconds.