The generator matrix

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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+84x^62+354x^63+567x^64+1086x^65+1331x^66+1670x^67+1922x^68+2572x^69+2562x^70+3014x^71+2595x^72+3216x^73+2466x^74+2434x^75+1904x^76+1712x^77+1197x^78+860x^79+511x^80+350x^81+149x^82+112x^83+47x^84+20x^85+17x^86+4x^87+2x^88+4x^89+1x^90+3x^92+1x^98

The gray image is a linear code over GF(2) with n=288, k=15 and d=124.
This code was found by Heurico 1.16 in 47.4 seconds.