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  1  1  1  1  1  1  X X^2 X^2  X  X  X X^2  X  X X^2 X^2  1 X^2  1  0  1  1  X X^2  1  X  X  1  1  0  1  1  X  X  X
 0  X  0  0  0  0  0  0  0  0 X^2  X  X X^2+X  0 X^2+X X^2+X  0  X X^2 X^2+X X^2  X  X  X X^2  X  0  X X^2 X^2+X  X X^2+X  0 X^2  0 X^2 X^2  X X^2+X  X  X X^2  X  X X^2  0 X^2+X X^2  X X^2 X^2+X  X  X  0  X X^2+X X^2 X^2+X  0  0  0 X^2  0 X^2 X^2+X X^2  X  X X^2+X X^2+X X^2  X
 0  0  X  0  0  0  0  0  0  0 X^2+X X^2  X  X  X  X  0  X  0  X X^2+X X^2  0 X^2+X  X  X X^2+X X^2+X X^2  0 X^2+X  0 X^2  X  0 X^2+X  X X^2  0 X^2 X^2+X  X X^2+X X^2+X  0 X^2 X^2 X^2  X X^2 X^2+X X^2 X^2 X^2 X^2+X  0 X^2  X  0 X^2 X^2  X X^2 X^2+X X^2+X  X X^2 X^2  0 X^2  X X^2+X X^2
 0  0  0  X  0  0  0  X X^2+X  X  X X^2+X  0  X X^2  0 X^2+X X^2+X X^2+X X^2 X^2+X  X  0 X^2  0 X^2  X  X  X X^2  X  0 X^2  X X^2 X^2  X X^2  X X^2  X X^2  0  0 X^2  0  X X^2  0  0 X^2 X^2+X  X X^2+X  X X^2+X  0  0 X^2+X  X  0  X X^2+X  X  X  X X^2 X^2 X^2+X X^2  0 X^2 X^2
 0  0  0  0  X  0  X  X  X X^2  X  X  X X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X  X X^2+X X^2 X^2  X  0 X^2+X X^2 X^2+X X^2+X  X  X  X X^2+X  X X^2  0  0  0  X  X  X  0 X^2+X  X  X X^2+X  0 X^2 X^2  X  0  0 X^2 X^2+X X^2  X  0  0 X^2+X X^2+X X^2+X  X X^2+X X^2  X X^2+X X^2+X X^2+X X^2+X  X  X
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  X  X X^2+X  0  X X^2 X^2 X^2 X^2+X  X  0 X^2 X^2  0  X  0  X X^2 X^2 X^2+X X^2+X X^2+X X^2+X 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^2 X^2 X^2  X X^2+X X^2+X  0 X^2+X X^2+X X^2  0 X^2+X  X X^2 X^2+X  0 X^2 X^2 X^2 X^2 X^2  0  X X^2+X X^2+X  0  0  X X^2  0 X^2
 0  0  0  0  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  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  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+214x^62+8x^63+589x^64+64x^65+862x^66+208x^67+1079x^68+512x^69+1553x^70+772x^71+1860x^72+932x^73+1995x^74+844x^75+1504x^76+476x^77+1120x^78+212x^79+684x^80+60x^81+404x^82+4x^83+263x^84+4x^85+105x^86+33x^88+19x^90+2x^92+1x^104

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 36.5 seconds.