The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  1  1 X^2  1 X^2  0  1  0  1  X  1  1 X^2  1  1  1  1  1  X  0  1  1  0  1  X  X  1  0  X  1  1 X^2  1  1  0 X^2  1  1  1
 0  X  0  X  0  0  X X^2+X  0 X^2 X^2+X  X  0  X  X X^2 X^2 X^2+X  0  X X^2+X  0  X X^2  X  X X^2 X^2+X  0 X^2+X  X X^2  0  X  0  X  0  X  0 X^2  X  0 X^2 X^2+X  X  X  X  0  X  0 X^2  X  X X^2 X^2 X^2 X^2+X  X  0 X^2  X  X  0 X^2  X X^2+X X^2 X^2  0 X^2 X^2  0
 0  0  X  X  0 X^2+X  X  0 X^2  X  0  X  0 X^2+X X^2  X  X X^2  0 X^2+X X^2+X  X X^2  0  X X^2  X X^2+X  X  0 X^2+X  0 X^2+X X^2+X  0 X^2+X X^2 X^2+X  X  X  0  X  X  X X^2 X^2+X X^2 X^2+X X^2 X^2 X^2+X X^2+X X^2+X X^2+X  X  X X^2  X X^2+X X^2  X  X  0 X^2  X  X  0  X  X X^2+X  X  0
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 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
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 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  0 X^2 X^2  0  0  0  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+28x^62+42x^63+107x^64+134x^65+175x^66+204x^67+239x^68+288x^69+334x^70+412x^71+365x^72+340x^73+313x^74+246x^75+211x^76+206x^77+121x^78+96x^79+59x^80+44x^81+35x^82+22x^83+29x^84+10x^85+12x^86+2x^87+11x^88+2x^89+4x^90+1x^92+1x^94+1x^96+1x^106

The gray image is a linear code over GF(2) with n=288, k=12 and d=124.
This code was found by Heurico 1.16 in 1.61 seconds.