The generator matrix

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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+328x^63+730x^64+976x^65+1347x^66+1856x^67+2015x^68+2422x^69+2494x^70+2894x^71+2735x^72+2976x^73+2689x^74+2446x^75+1914x^76+1688x^77+1142x^78+824x^79+544x^80+352x^81+190x^82+110x^83+53x^84+18x^85+10x^86+6x^87+8x^88

The gray image is a linear code over GF(2) with n=288, k=15 and d=126.
This code was found by Heurico 1.13 in 52.5 seconds.