The generator matrix

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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+66x^65+136x^66+318x^67+282x^68+562x^69+390x^70+780x^71+498x^72+866x^73+566x^74+892x^75+497x^76+762x^77+311x^78+472x^79+195x^80+258x^81+94x^82+86x^83+42x^84+34x^85+30x^86+12x^87+18x^88+10x^89+4x^90+3x^92+2x^93+5x^94

The gray image is a linear code over GF(2) with n=296, k=13 and d=130.
This code was found by Heurico 1.16 in 5.35 seconds.