The generator matrix

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

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+19x^62+50x^63+122x^64+142x^65+339x^66+304x^67+699x^68+592x^69+1257x^70+900x^71+1766x^72+1096x^73+1956x^74+1164x^75+1723x^76+852x^77+1192x^78+502x^79+686x^80+322x^81+301x^82+132x^83+81x^84+60x^85+37x^86+20x^87+30x^88+8x^89+10x^90+9x^92+7x^94+3x^96+2x^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 18.1 seconds.