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

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+167x^62+12x^63+402x^64+40x^65+523x^66+188x^67+714x^68+244x^69+864x^70+612x^71+942x^72+372x^73+852x^74+404x^75+658x^76+92x^77+470x^78+64x^79+245x^80+20x^81+157x^82+89x^84+34x^86+18x^88+4x^90+2x^92+1x^94+1x^100

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 15.6 seconds.