The generator matrix

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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+270x^67+428x^68+520x^69+679x^70+808x^71+622x^72+736x^73+654x^74+632x^75+462x^76+602x^77+474x^78+384x^79+314x^80+240x^81+126x^82+100x^83+52x^84+42x^85+16x^86+12x^87+9x^88+4x^89+2x^90+2x^91+1x^94

The gray image is a linear code over GF(2) with n=296, k=13 and d=134.
This code was found by Heurico 1.16 in 28.5 seconds.