The generator matrix

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

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+170x^31+324x^32+466x^33+431x^34+504x^35+503x^36+476x^37+340x^38+314x^39+223x^40+202x^41+83x^42+36x^43+13x^44+8x^45+2x^46

The gray image is a linear code over GF(2) with n=144, k=12 and d=62.
This code was found by Heurico 1.16 in 0.306 seconds.