The generator matrix

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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+68x^60+394x^61+913x^62+1546x^63+2770x^64+3364x^65+5109x^66+5832x^67+7910x^68+8838x^69+11174x^70+10518x^71+13183x^72+11020x^73+11535x^74+9098x^75+8855x^76+5712x^77+4886x^78+3276x^79+2100x^80+1226x^81+808x^82+478x^83+219x^84+96x^85+63x^86+36x^87+30x^88+6x^89+8x^90

The gray image is a linear code over GF(2) with n=288, k=17 and d=120.
This code was found by Heurico 1.13 in 227 seconds.