The generator matrix

 1  0  0  0  0  1  1  1 X^2+X  1  1  1  X  1 X^2+X X^2+X  1  X X^2 X^2+X  1  1  1  1  0  0  0  1  1  1  1  1  1  1  1  1
 0  1  0  0  0  0 X^2  0 X^2  0 X^2+1 X^2+X+1  1 X^2+X  1  1 X^2  1  1  X X^2+X+1 X^2+X+1 X+1 X+1 X^2+X  1  1 X^2+1 X^2+X X^2+1 X+1 X^2+1 X^2 X+1  X X^2+X
 0  0  1  0  0  0  0 X^2 X^2  1  1  0 X^2+1 X+1  X X^2+X  1 X^2+X+1 X^2+X+1  1 X^2+1 X^2 X+1  X  1  0 X^2+1 X^2+X+1 X^2 X^2+X X+1 X+1 X^2+X X^2+1  X X+1
 0  0  0  1  0  1  X X+1  1  1 X^2  0  0  X X^2+X+1 X+1 X^2+X+1  1 X^2+X X^2 X^2+1 X^2+1  0 X+1 X^2+1  0 X+1 X+1 X+1 X^2+X X^2+X  X X^2 X^2+X+1  X X^2
 0  0  0  0  1  1 X+1  X X+1 X^2 X^2+X X+1 X+1 X^2+X+1  0 X^2+1 X^2+X+1 X^2+1 X^2+X  1  1 X+1  1  0 X+1 X+1  X X^2+X X^2+1  1  X  1 X^2+X X+1  1 X^2+X+1
 0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 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  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+153x^28+670x^29+1466x^30+2386x^31+3654x^32+5164x^33+6621x^34+7942x^35+8777x^36+8440x^37+7013x^38+5370x^39+3637x^40+2148x^41+1175x^42+546x^43+218x^44+90x^45+45x^46+12x^47+8x^48

The gray image is a linear code over GF(2) with n=144, k=16 and d=56.
This code was found by Heurico 1.13 in 23.7 seconds.