The generator matrix

 1  0  0  0  0  1  1  1  0  1 X^2  1  1 X^2+X  0  X  X  1  0  1  1  1  X  1  1  1 X^2  0  1 X^2  X  1  X  1  1  X X^2  1 X^2  1  1  0  1 X^2+X  X  1  1  1  0 X^2+X  1  0 X^2+X X^2  1  1 X^2  1  1  1  1  0  X  0 X^2+X  1  X  0 X^2+X  1  X  0 X^2  1
 0  1  0  0  0  0 X+1  X X^2 X+1  1 X^2  1  1  1  1  1 X^2+1  1 X^2+X+1 X^2+1 X^2+1  X  X X^2+1  X X^2+X X^2+X  0  1  1 X+1  1 X^2+X  0 X^2+X  1 X+1 X^2+X X+1 X^2+1  1 X^2+X  1  X  0 X+1 X^2+X  1 X^2 X^2+1  X  1 X^2+X  0  0  1  1  X X^2+X+1  X  X  1  X X^2 X^2+X X^2+X  1  1  0  1  1  1  0
 0  0  1  0  0  0  1 X+1  1 X^2+1 X^2 X^2+1  1 X+1 X^2+X X^2+1 X^2+X  0  1 X^2  0  X  1 X+1 X^2+X+1  X  1  0 X^2 X^2+1 X^2+1  0 X^2+X+1  X X^2+1  1  X X+1  0  1  X X^2+X+1 X+1 X^2+X  1 X+1 X^2+X+1 X^2+1 X^2+X+1  1 X^2+1  X  X  X X^2+X+1 X^2+X X^2+X+1 X^2+X+1 X^2 X^2+X  X  1 X+1 X^2  X X^2+X+1  1  1 X+1  0 X+1 X+1  1  0
 0  0  0  1  0  1 X^2 X^2+1  1 X+1 X^2+1 X^2+X  X X^2+X+1  X X^2+X X+1  0 X^2 X^2+X+1  X X^2+X+1  0  X X+1 X^2+1 X^2+1  1  X X^2+X+1 X^2+X+1  X  X X+1 X^2+X+1 X+1 X^2+1 X+1  1 X^2+X  0 X^2 X^2+X  0 X^2+X  X  0  1  1  1 X^2+1  1  1  1 X^2+X X^2 X^2+X X^2+X+1  1  X  X  X X^2+X X^2  1  0  0 X^2+X X+1 X^2+X+1  X X+1  1  0
 0  0  0  0  1  1 X^2+1  X X+1 X^2+1 X^2+X X^2+1  0  0 X^2+1  1 X^2+X+1 X^2+X  X  0 X^2+1 X^2+1 X^2+1  X X^2  0  X X^2+1 X^2+X+1  1 X^2+X X^2+1 X+1  1  1 X^2 X^2  0 X+1 X^2+X+1  X  X X^2+1 X^2 X^2  0 X+1 X^2+X X+1 X^2+1 X^2+X+1  0 X+1  1 X^2+X  1 X^2+X+1  X X^2+X+1  1  1 X^2  X  1  1 X^2 X+1 X^2+1  1  X  1  X X+1  0
 0  0  0  0  0  X  0  X  X X^2+X  X X^2 X^2 X^2+X X^2 X^2 X^2+X  0  0 X^2+X X^2 X^2+X  0 X^2  X X^2+X X^2+X X^2+X  0  X  X  0  0  X  0  0  0 X^2  0  X  X X^2+X  X X^2+X X^2+X  X X^2+X X^2 X^2 X^2  0 X^2 X^2  0  X X^2+X  0  0 X^2+X X^2+X  0  X  X  X  0  X X^2  0 X^2  0 X^2+X X^2  X 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+416x^63+861x^64+1688x^65+2402x^66+3658x^67+4729x^68+6622x^69+7522x^70+9240x^71+9937x^72+11972x^73+11764x^74+12158x^75+10944x^76+9866x^77+7793x^78+6576x^79+4362x^80+3294x^81+2094x^82+1498x^83+701x^84+436x^85+220x^86+112x^87+77x^88+38x^89+12x^90+6x^91+2x^92+4x^93+1x^94+2x^96

The gray image is a linear code over GF(2) with n=296, k=17 and d=124.
This code was found by Heurico 1.13 in 234 seconds.