The generator matrix

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

generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+74x^62+40x^63+297x^64+160x^65+520x^66+472x^67+863x^68+1064x^69+1078x^70+1456x^71+1320x^72+1792x^73+1356x^74+1552x^75+1060x^76+912x^77+787x^78+552x^79+399x^80+160x^81+210x^82+24x^83+124x^84+8x^85+52x^86+22x^88+16x^90+8x^92+1x^94+1x^96+2x^98+1x^100

The gray image is a linear code over GF(2) with n=292, k=14 and d=124.
This code was found by Heurico 1.16 in 18.5 seconds.