The generator matrix

 1  0  1  1  1 X^2+X  1  1  X  1  1 X^2 X^2+X  1 X^2+X  1  1  1  0  1  1  1  1 X^2 X^2 X^2+X X^2  X  0 X^2+X X^2  X  1  1  1  1  1  1  1  1  1  1 X^2  X  X  1  1 X^2+X  0  1  1 X^2 X^2+X X^2  0  1  1  1  1  1  1  1  1  1  1  1  0  X  1  1  X  1
 0  1  1 X^2+X X^2+X+1  1 X^2 X+1  1  X X^2+1  1  1  0  1 X+1  0 X+1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  0 X^2+X X^2  X X+1 X^2+1  0 X^2+X  0 X^2+X  1  1 X^2+X X^2+X+1  1  1  1 X^2+1 X^2+X  1  1  1  1  0  1 X^2+X X^2+X+1 X^2+X+1 X^2+X X^2+X X+1 X+1  X X^2+X  1  X X^2+1 X^2  1 X^2+X+1
 0  0  X  0 X^2+X  0  X X^2  X X^2+X  0 X^2+X X^2 X^2  X X^2  X  X  0 X^2+X  0 X^2 X^2+X X^2+X X^2  0  X  X  0  0  X  X  0  0  X  X X^2 X^2  0  0  X  X  0 X^2 X^2+X X^2+X X^2+X  X  X X^2+X X^2+X X^2+X X^2+X X^2+X  X X^2  X  X  0 X^2+X  0 X^2 X^2  0 X^2+X  X X^2 X^2+X  X X^2+X  X X^2
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0
 0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 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+126x^66+120x^67+168x^68+232x^69+159x^70+188x^71+194x^72+180x^73+123x^74+176x^75+110x^76+80x^77+89x^78+28x^79+20x^80+20x^81+11x^82+12x^84+4x^86+5x^88+1x^92+1x^100

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 0.465 seconds.