The generator matrix

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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+176x^66+360x^67+408x^68+402x^69+390x^70+368x^71+300x^72+324x^73+289x^74+244x^75+193x^76+182x^77+156x^78+80x^79+73x^80+64x^81+41x^82+20x^83+17x^84+4x^85+4x^86

The gray image is a linear code over GF(2) with n=288, k=12 and d=132.
This code was found by Heurico 1.16 in 0.785 seconds.