The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  X  1 X^2  1 X^2  1  1  1  X  1  X  1  1  X  1  0 X^2  1  1  1  1  1  1  X X^2  1 X^2  1  1 X^2  X  1  1  1  X  1  1 X^2  X  1  0  1  1  1 X^2+X  0  X X^2 X^2+X X^2+X X^2  1  1  0  0  1  1  0  1 X^2  1
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X X^2+1  1  0  1  1  1 X^2 X+1 X+1  1 X^2+X  1  0 X+1  1  X  1  1 X^2+1 X^2+1 X^2+1  0  X  0  1  1 X^2+1  1 X^2  0  1  1 X^2+1 X^2+X  1  1  X X^2  1  1 X+1  1 X+1 X^2+1  0  1  1  X  0  1  1  0  1  0  X  1 X^2+1 X^2+X  X  1  1  0
 0  0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2+X X^2  X X^2  X  X  0 X^2+X X^2 X^2+X X^2+X X^2  0 X^2+X  0  X  X  0 X^2  0 X^2+X  X  0 X^2+X X^2  0 X^2+X  0 X^2+X X^2+X X^2+X  X  X X^2  0  0 X^2+X  X X^2+X X^2 X^2 X^2+X  X X^2 X^2  0  0  0 X^2+X  X X^2+X X^2+X  X  X  0 X^2+X X^2+X X^2 X^2+X X^2+X  X X^2+X  0
 0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0
 0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 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 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  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+24x^62+60x^63+210x^64+160x^65+480x^66+258x^67+782x^68+288x^69+1064x^70+302x^71+1108x^72+276x^73+1052x^74+264x^75+769x^76+204x^77+376x^78+116x^79+168x^80+76x^81+60x^82+22x^83+24x^84+20x^85+4x^86+2x^87+8x^88+8x^90+1x^92+4x^94+1x^96

The gray image is a linear code over GF(2) with n=288, k=13 and d=124.
This code was found by Heurico 1.16 in 4.73 seconds.