The generator matrix

 1  0  0  0  1  1  1  0  0 X^2 X^2  1  1  1  1  X  1  1  1  1  X  0 X^2+X X^2  1  1  1  X  1  1  1 X^2+X  1  1 X^2+X  X  1  1 X^2 X^2  X  0  0  1  0  0  1  1  1  X  1  1  1  1  1  1 X^2+X  X  X X^2+X X^2+X  X  1  1  1  1 X^2  1  0  1 X^2  1
 0  1  0  0  0  1  1  1 X^2  1  1  0  1 X+1 X^2 X^2+X X^2+X+1 X+1 X^2+X  1  1  X  1 X^2+X  X  X X+1  1  0 X^2+1 X^2+X+1  1  1  0 X^2+X  0 X^2 X^2+1  0  1  1  1 X^2+X  1  X X^2 X^2 X^2+X X^2+X+1  1  1 X+1 X^2+X X^2+X+1  X X+1  1 X^2+X X^2  1  1 X^2+X X^2+X+1 X^2+1 X^2+1  X  1  X  1  1  0 X^2
 0  0  1  0  1 X^2 X^2+1  1  1  0  1 X^2  1 X^2 X^2+1  1  1  0  1 X+1 X+1  1 X^2  X  X X^2+1 X^2+X  0 X^2+1 X+1  0 X^2 X^2+X+1  X  1  1  X  1  X X^2 X^2+X  0  1 X^2+X X^2+X  1 X^2+X+1 X^2 X^2+X X^2+1 X^2 X^2+X X^2+X+1 X+1 X^2+1 X+1 X^2+X+1  X  1  X X^2+X  1 X+1  X X^2+X+1 X^2+X X+1  X X^2+X X^2+X  1 X^2+1
 0  0  0  1 X^2  0 X^2 X^2  1  1 X^2+1  1  1 X+1  1  0  X X^2+X X^2+X X^2+X+1  0 X+1 X^2+X+1  1  1 X^2+1 X^2+X+1 X^2+X X^2+X X^2 X^2+1 X^2+1  1  0  X  1 X+1 X^2+X+1  1 X^2+X X^2+X+1 X+1  0  0  1 X^2+X X^2 X^2+1 X^2+X  X X+1  1 X^2+X X+1 X^2+X+1 X^2+X X^2+X  1 X^2+X+1 X^2  1 X^2+X+1  0 X^2+1  X  0 X^2 X^2+X+1 X+1 X^2+X  1 X+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+182x^66+308x^67+376x^68+430x^69+485x^70+378x^71+363x^72+254x^73+267x^74+190x^75+211x^76+162x^77+131x^78+122x^79+89x^80+62x^81+55x^82+10x^83+7x^84+4x^85+8x^86+1x^88

The gray image is a linear code over GF(2) with n=288, k=12 and d=132.
This code was found by Heurico 1.11 in 0.36 seconds.