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  1  1  0  0  0 X^2 X^2  X X^2 X^2  X  0  X  X  X  1 X^2  0  X  X  0  1 X^2 X^2  1  1  1  1  X  1
 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^2  X X^2+X X^2  X  X  X X^2  X  0  X X^2 X^2+X  X X^2+X X^2+X X^2+X X^2+X  X X^2  0 X^2+X X^2+X X^2  X X^2+X  X  0 X^2  X  0  X X^2 X^2+X  X  X  0  X X^2  0  X X^2+X  X  X  X X^2  0 X^2+X  0  X X^2+X X^2+X X^2+X  X X^2 X^2
 0  0  X  0  0  0  0  0  0  0 X^2+X X^2  X  X  X  X  0  X  X  0 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^2+X  X  0 X^2 X^2  X  0 X^2  X X^2+X X^2+X  X  X  0 X^2  X X^2 X^2 X^2+X  0 X^2 X^2 X^2+X X^2 X^2+X  0  X  0 X^2+X X^2+X X^2+X  X  0 X^2  0  0 X^2  0  X  X  0
 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^2+X X^2+X  X  0 X^2  0 X^2  X  X  X X^2  X  0 X^2+X  0  X X^2+X  0 X^2  X  X X^2 X^2+X  0 X^2  X  0  0  X X^2  X X^2 X^2+X X^2 X^2  0 X^2+X  0 X^2 X^2  X  0 X^2  X  0 X^2+X  0  X X^2+X X^2  0 X^2+X X^2 X^2+X  X
 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 X^2 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^2+X  X  0 X^2+X X^2+X  0  0 X^2  X X^2  0 X^2+X X^2 X^2  X X^2  0 X^2+X  X X^2+X  X  X X^2  0  X X^2+X  X X^2+X X^2+X X^2+X  0 X^2+X  X X^2  X  0 X^2 X^2+X  X  0 X^2+X X^2+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 X^2+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  0 X^2 X^2 X^2 X^2  0  0 X^2+X X^2+X X^2+X X^2+X  X  X X^2  X X^2  X  X  X  0 X^2  X X^2 X^2+X  0 X^2+X X^2  X X^2 X^2+X  0  0 X^2 X^2  X  X  0 X^2+X  0  0 X^2+X
 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  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0 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+64x^62+134x^63+202x^64+270x^65+377x^66+482x^67+553x^68+702x^69+907x^70+1166x^71+1289x^72+1332x^73+1462x^74+1490x^75+1276x^76+1118x^77+883x^78+672x^79+568x^80+384x^81+304x^82+204x^83+172x^84+140x^85+86x^86+68x^87+32x^88+22x^89+12x^90+8x^91+3x^92+1x^106

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 25.5 seconds.