The generator matrix

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

generates a code of length 36 over Z2[X]/(X^3) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+304x^29+801x^30+1176x^31+1993x^32+2680x^33+3221x^34+4000x^35+4174x^36+4114x^37+3597x^38+2664x^39+1906x^40+1164x^41+563x^42+218x^43+116x^44+58x^45+10x^46+4x^47+2x^51+2x^52

The gray image is a linear code over GF(2) with n=144, k=15 and d=58.
This code was found by Heurico 1.16 in 46.8 seconds.