The generator matrix

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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+206x^69+144x^70+352x^71+77x^72+348x^73+132x^74+236x^75+46x^76+164x^77+50x^78+72x^79+25x^80+76x^81+19x^82+44x^83+10x^84+38x^85+6x^86+1x^88+1x^98

The gray image is a linear code over GF(2) with n=296, k=11 and d=138.
This code was found by Heurico 1.16 in 0.506 seconds.