The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1 X^2+X  0 X^2  X  1  X X^2  1  X  1  1  1  1  0  1  1 X^2  1 X^2+X  X  1  1  1  X X^2+X  1  X  1  1  1  1  X  0 X^2  X  1  X X^2+X X^2+X  1 X^2+X X^2  1  1  1  1  0  1  0  0 X^2  1  1 X^2+X  1  0  X X^2+X  1  1  1  0
 0  1  0  0  1 X^2  1  1 X^2+1  0 X^2+X+1  X  1  X  1  1 X+1  X  1  0 X^2+X  X X^2 X^2+1 X^2+X  0 X+1 X+1  1 X^2  1  X  0 X^2  1 X^2+X X^2 X^2+X  1  X X^2+X+1 X^2+X  0  1  1  X  1 X^2+1  1  1  1 X+1  1  1  1 X+1  0  X  X X^2+X  1  1  1 X^2+X  0  1 X^2+X+1 X^2+X  1  1 X^2+X+1  X  0  0
 0  0  1  0  X  0 X^2+X  X  1  1 X+1 X^2+X+1  1  1 X+1 X^2+X X^2  1  1 X^2+X+1  1  1 X^2+X X^2 X^2 X^2+X X+1 X^2+1  0  0 X^2+X+1  1  X  1  X  X  1  0  1 X^2+X  X X+1  1  0  0  1 X^2+X+1 X^2+X+1 X^2 X+1 X^2  0  0 X^2 X^2  X  1 X^2+1  1 X^2+X  X X+1 X+1 X^2+X+1  X  X X^2+X  0  1 X+1 X+1  X X^2+X  X
 0  0  0  1  X  1 X+1 X+1 X+1  X  0  1 X+1 X^2+1 X^2  X X^2+X  0  0 X^2+X  1 X+1 X^2+X X^2+X+1 X^2+1  1 X+1 X^2  1  X X^2+1 X+1 X^2+1 X^2+1  1  1 X^2+X  X X^2+X X^2+1 X^2+X X^2+X X^2+X+1 X^2+1  X X^2+X X^2+X+1 X+1 X^2  X X^2+X X^2+X X^2+X+1 X^2+X+1  X X^2 X^2  X  1  X X^2+X+1  1  X  1 X^2+1 X^2+1 X^2+X+1  1 X^2+X+1 X^2+X X^2+X X+1 X^2+X  1
 0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  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+348x^67+178x^68+866x^69+380x^70+1024x^71+393x^72+1004x^73+325x^74+958x^75+301x^76+796x^77+192x^78+618x^79+146x^80+310x^81+84x^82+132x^83+33x^84+62x^85+8x^86+18x^87+4x^88+2x^89+3x^90+6x^91

The gray image is a linear code over GF(2) with n=296, k=13 and d=134.
This code was found by Heurico 1.11 in 21.2 seconds.