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  1  X  1  0  1 X^2+X  1  1  X  1  1  1 X^2 X^2+X  1  1 X^2  1  1  1  1  1  0 X^2  1  1 X^2+X  1 X^2  X X^2+X X^2+X  1  1  X X^2+X  0  1 X^2  0  1  1  0  X  1  1  1  1 X^2+X  1 X^2  1  0  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^2+X  X X^2  1 X^2+1  1  X  X  1 X^2+X+1 X^2 X^2+X+1  X  1  1 X^2+X+1 X^2 X+1 X^2+X  X  0  1  1  0  1  0  1 X^2+1 X^2+X  1  X  1  0  0  X X^2+X  1 X^2 X^2+X  1 X^2+X+1 X^2  0 X^2 X^2+X  1  X X+1  0 X+1  1 X^2+1  1  0
 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 X^2+X+1  1  1  0  X X^2+X X^2+X  0 X^2+1 X^2+X+1 X^2  1  1 X^2+1 X+1 X^2  X X^2+X  1 X^2 X^2 X^2+1 X^2+X+1 X^2 X^2  X X^2 X^2+X  1 X^2+X X^2 X^2 X^2+X X^2+X+1 X^2+X  1  1 X+1 X^2 X^2+X  0 X+1  1  1  1 X^2+X X^2+X X^2+X  0  0 X^2+X X^2+X+1 X^2+1  0
 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  1  0 X^2+X+1 X+1 X^2+1  X  0 X^2+X X^2+1 X+1  X  0  1 X+1 X^2 X^2+1  X X^2  0 X^2+X+1 X+1 X^2+X+1  X  1  1 X+1 X^2+X+1 X^2+X+1 X^2+X+1 X^2 X^2+X  1 X^2+1 X^2+1 X^2+X  1  1 X^2+X+1 X^2+X  1 X^2 X^2+1 X^2+X+1 X^2+X+1 X^2+1 X^2 X^2+X+1 X^2+1  X  1 X+1  X X^2+X+1 X^2+X+1  0
 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+1 X^2+X X^2+X X^2+X+1  X X^2+X X^2+X+1  1 X^2  1 X^2+X+1 X^2+X X^2+X X+1 X^2+X X^2+X+1 X^2+1  1  0 X^2+X  0 X^2+1 X+1  0  1 X^2  X  1 X^2+X+1 X^2+X+1 X^2+X+1  1  0 X^2+X+1 X^2 X+1 X^2+X  1 X^2+1 X+1 X^2+X+1  1 X^2  X X^2+1  0 X^2  0  X X^2+X X^2+X  1 X+1 X+1  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+82x^62+312x^63+649x^64+1166x^65+1417x^66+1700x^67+1895x^68+2462x^69+2541x^70+2898x^71+2790x^72+2840x^73+2542x^74+2440x^75+1927x^76+1638x^77+1227x^78+988x^79+550x^80+300x^81+183x^82+120x^83+52x^84+20x^85+8x^86+4x^87+8x^88+6x^89+2x^95

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 44 seconds.