The generator matrix

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

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+216x^31+191x^32+638x^33+204x^34+756x^35+302x^36+670x^37+136x^38+516x^39+126x^40+218x^41+44x^42+44x^43+18x^44+10x^45+4x^47+2x^48

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 20.9 seconds.