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  1  0  0  1  1  1  1  0  1  1  X  1  1  X  X  0  1
 0  X  0  0  0  X X^2+X  X  0 X^2  X X^2+X  0 X^2  X  X  0 X^2  X  X X^2+X X^2 X^2+X  0 X^2+X  X X^2  0 X^2 X^2+X  X  0 X^2 X^2 X^2  X X^2 X^2+X X^2+X X^2+X X^2+X  X  X  X  0  0  0  0  0  X  X  0 X^2 X^2 X^2 X^2  X  X  0  0  0 X^2  X X^2+X X^2 X^2+X X^2+X X^2 X^2  0  0  X
 0  0  X  0  X  X  X X^2  0 X^2 X^2+X X^2+X  X  X X^2 X^2  0 X^2+X  0  X  X  X  0  0 X^2+X X^2+X X^2+X X^2  0 X^2  0  X  X X^2+X X^2  X  0  0  0 X^2 X^2 X^2+X X^2+X  X  X X^2 X^2+X  0  0 X^2+X  X X^2 X^2+X  X  0 X^2  0 X^2  X X^2+X X^2 X^2 X^2  X  0  0  X  0 X^2+X X^2+X  0  X
 0  0  0  X  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2+X  X  0  X  0 X^2 X^2+X X^2+X  0 X^2+X X^2  0 X^2+X  0  X  X X^2 X^2+X X^2+X  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2+X  0  X  0  X X^2+X X^2+X  X  X X^2+X X^2 X^2  0  0  X X^2+X X^2+X  X X^2  0 X^2+X  X  X X^2  0  0  0 X^2 X^2  X  X  0  X  0
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2  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+37x^66+56x^67+62x^68+64x^69+183x^70+18x^71+238x^72+18x^73+152x^74+46x^75+56x^76+38x^77+6x^78+6x^79+25x^80+6x^81+2x^82+2x^83+2x^84+2x^85+3x^86+1x^130

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 0.312 seconds.