The generator matrix

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

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+60x^66+103x^68+16x^69+147x^70+112x^71+187x^72+112x^73+128x^74+16x^75+58x^76+48x^78+31x^80+3x^84+1x^86+1x^136

The gray image is a linear code over GF(2) with n=288, k=10 and d=132.
This code was found by Heurico 1.16 in 0.315 seconds.