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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+78x^62+138x^63+200x^64+280x^65+372x^66+562x^67+563x^68+820x^69+982x^70+1012x^71+1311x^72+1252x^73+1315x^74+1394x^75+1217x^76+1100x^77+907x^78+694x^79+596x^80+492x^81+355x^82+226x^83+157x^84+128x^85+72x^86+60x^87+43x^88+24x^89+13x^90+10x^91+7x^92+1x^94+1x^96+1x^98

The gray image is a linear code over GF(2) with n=296, k=14 and d=124.
This code was found by Heurico 1.16 in 25.2 seconds.