The generator matrix

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

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+119x^66+116x^67+224x^68+154x^69+235x^70+138x^71+205x^72+130x^73+225x^74+112x^75+102x^76+90x^77+107x^78+18x^79+34x^80+12x^82+4x^84+8x^85+2x^86+6x^88+2x^89+2x^90+1x^94+1x^102

The gray image is a linear code over GF(2) with n=288, k=11 and d=132.
This code was found by Heurico 1.16 in 0.459 seconds.