The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1 X^2+X  1  1  0 X^2+X  1  1  1  1 X^2+X  1 X^2  1  1  1  1 X^2+X  X  1  1  1  1 X^2  1  1 X^2+X  1  0  0 X^2+X  1 X^2  1  X X^2  1  1  1  1 X^2 X^2  1  1  1  1  1  1 X^2+X  1  0  1  1  1 X^2+X  1  1  X  X
 0  1  1  0 X^2+X+1  1  X X+1  1 X^2+1  1 X^2+X  0 X^2+X+1  1 X^2+X  1  1  1 X+1 X^2 X^2+X  1  1 X^2+X  1 X+1 X^2  1 X^2+X+1  1  1  0  1  X X+1  1  0 X^2+X  1 X^2+1  1  1  1  1  1 X^2  1  1 X^2+X X^2+X X^2+1 X^2+1  1  1 X^2+X+1 X^2  X X^2+1  0 X^2+1  1 X^2+X+1  X  0 X+1 X+1  1 X^2+X X^2+X+1  1  X
 0  0  X  0 X^2+X  0  0  X  0 X^2+X  0  0  X X^2 X^2+X  X  0  X X^2+X  0  X X^2+X X^2 X^2+X  X  X X^2+X X^2  X  0  X  X X^2+X X^2 X^2 X^2+X  X  X  X X^2  X  0 X^2+X  0 X^2  0  X  0 X^2  0 X^2+X  0  X X^2  X  X  X X^2 X^2  0  X X^2+X X^2+X X^2+X  X X^2+X X^2  0 X^2+X X^2  X  X
 0  0  0  X  0  0  X  X  X  X X^2+X X^2  X X^2+X X^2+X  X  X  X  0 X^2  0 X^2 X^2  0  0  0  X X^2+X X^2  0  X X^2  X X^2+X  X  0  0 X^2 X^2+X  0  X X^2+X X^2 X^2+X  0  X  X  0  X X^2  0 X^2+X X^2 X^2  X X^2 X^2+X X^2+X  X  0 X^2 X^2  X  0  X  0 X^2  X  0  X  0 X^2
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  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 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  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+183x^62+28x^63+454x^64+252x^65+801x^66+516x^67+1329x^68+1012x^69+1556x^70+1276x^71+1741x^72+1228x^73+1604x^74+1036x^75+1165x^76+540x^77+760x^78+216x^79+322x^80+40x^81+173x^82+87x^84+36x^86+17x^88+6x^90+3x^92+1x^94+1x^96

The gray image is a linear code over GF(2) with n=288, k=14 and d=124.
This code was found by Heurico 1.16 in 65.4 seconds.