The generator matrix

 1  0  0  0  0  1  1  1  0 X^2  1  1 X^2+X  1  0  1  1 X^2+X  1 X^2+X X^2 X^2+X  1  X  1  1  0 X^2 X^2+X  X X^2  1 X^2+X  1  1  1  1  0  1 X^2  1 X^2  1  1  1  1  1 X^2  X  0  1  1  1  1  1  X  1 X^2+X  1  X  1 X^2+X  1  0 X^2  0  0  X  X  1 X^2  1
 0  1  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  1 X^2+1  1  1  1 X^2+X+1  1 X^2+X+1  1  1 X^2+X X^2+X  1  1 X^2+X+1  X  X X^2+1 X^2+1 X^2+1 X^2+X X^2+X  1 X^2 X^2 X^2+1 X^2+X+1 X+1  1 X^2+X  1  1  1 X^2+X+1 X^2  X  1  1  1 X^2+X+1 X^2+X X^2+X  0  X  X X+1  1  1  1  0  1  X X+1  X X^2+X
 0  0  1  0  0  0  1  1  1  1 X^2 X^2+1  1 X^2+X+1 X^2  0 X^2+X X+1 X^2  X X^2 X^2+X+1 X+1 X^2+1 X^2+X X^2+X X+1  1  X  0 X^2+X X^2  1 X^2+1 X^2+X+1 X^2+1 X^2+X X^2+X  X X+1  X X^2+X X+1 X+1 X^2 X^2+1  X  0 X^2 X+1 X+1 X^2+1  1  1 X^2  X X^2+X X^2 X^2+1  1 X^2  0 X^2+1  1 X^2+X+1  X  1  X  1 X^2  0  X
 0  0  0  1  0  1  1 X^2 X^2+1 X^2+1  X  X  X  1  1 X^2+X+1  X X^2+X+1 X^2+X X^2+X X^2+X+1  0  0  0 X^2+X+1 X^2 X^2+X+1  X  0 X+1 X^2  X X^2+1 X^2+1 X^2 X+1 X^2+1  1  1  1  0  1 X^2+X+1  1 X+1 X^2+X  1 X+1 X^2+X  X X^2+1 X+1  0  0 X^2 X^2+X+1 X^2+1  1  0 X^2 X+1  1  1 X^2+X+1  0 X^2+X+1 X^2+X X+1  1  0  1 X^2+X+1
 0  0  0  0  1  1 X^2 X^2+1 X^2+1  X X^2+X+1 X^2+X  1 X+1 X^2+X+1 X^2+X  0  0  0 X^2+X+1 X+1 X^2+X+1 X^2+1 X^2 X^2  1  1 X^2+1  1  X X^2+X+1 X^2 X^2+X+1 X^2+X  X  1 X+1 X+1  1 X^2+1 X^2+X+1  X X^2+X+1 X^2+X X+1 X^2+1 X^2 X^2+X X^2+X+1 X^2+X+1 X^2+X+1  X X^2+X X^2+X X+1 X+1 X^2  X X^2+X+1 X+1 X^2+1 X^2+X+1 X^2+X X+1 X^2+X+1  X X^2+X X^2+X X^2+X X^2+1  X  1
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 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  0 X^2  0 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  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+348x^62+644x^63+1656x^64+1540x^65+2909x^66+2932x^67+4418x^68+4124x^69+5663x^70+5024x^71+6490x^72+5148x^73+6274x^74+4392x^75+4596x^76+2752x^77+2794x^78+1408x^79+1121x^80+568x^81+391x^82+124x^83+126x^84+12x^85+49x^86+4x^87+20x^88+2x^90+4x^92+2x^94

The gray image is a linear code over GF(2) with n=288, k=16 and d=124.
This code was found by Heurico 1.13 in 60.3 seconds.