The generator matrix

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

generates a code of length 36 over Z2[X]/(X^3) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+184x^31+334x^32+414x^33+527x^34+374x^35+555x^36+426x^37+398x^38+320x^39+277x^40+142x^41+75x^42+50x^43+9x^44+10x^45

The gray image is a linear code over GF(2) with n=144, k=12 and d=62.
This code was found by Heurico 1.11 in 0.125 seconds.