The generator matrix

 1  0  0  1  1  1  X X^2  1 X^2+X  1  1  1 X^2  1  1  0  X  1  0  1  0  1 X^2  X  1  1  1  1 X^2+X  1  1 X^2  1  1 X^2  1  1 X^2+X  1  0  1  1  0  1  1  1  1  X  1  1  X  1  1  0  1  X  1  1 X^2+X X^2+X X^2+X X^2+X  0  1  1  X  1  1  1  1 X^2+X  1  1
 0  1  0  0 X^2+1 X+1  1 X^2 X^2+X+1  1 X^2 X+1 X^2  1 X^2+X+1  0  1  1  1  0  0  1  1  1  0 X^2+1 X^2+X X^2  X  1  X  X  1 X^2 X+1  1  X  X  X X^2+X+1  X X^2+1  1  1  0 X^2+X X+1 X^2+X+1  1 X^2+1 X^2+X+1  1  1 X^2+X  1 X^2+1  1  0 X^2+X  X  1  0  0  1 X^2  X  X  X  X X+1 X+1  1  1 X^2
 0  0  1  1 X^2+1 X^2 X^2+1  1 X^2+X+1  0 X+1 X^2  0  1 X^2+X+1 X+1  0 X+1 X^2  1  X X^2 X^2+1 X+1  1 X^2 X^2+1  X  X  0 X^2+1 X^2+X X^2+X+1  1  0  X  0 X^2+X+1  1 X^2+X  1 X^2 X+1  X X^2+X X+1  X  1 X^2 X^2+X X^2+1 X^2+X X^2+X+1 X^2 X^2+X+1 X+1 X^2+1 X^2 X^2+X  1 X^2+X+1  1  1 X^2+X+1 X^2+X X^2+1  1 X^2+X+1 X+1 X^2+X X^2+1 X^2+X+1  0  X
 0  0  0  X  X  0  X  X  0  X  0 X^2+X X^2+X X^2 X^2+X X^2+X  X  X  0 X^2+X X^2 X^2 X^2  0 X^2 X^2+X  0  X  0 X^2+X X^2+X  X  X X^2 X^2  0  0 X^2+X  0 X^2 X^2+X  X X^2  X X^2+X  0 X^2+X  0 X^2  0  X X^2+X  X  X X^2  0  0 X^2 X^2 X^2+X  X X^2  X X^2+X  0 X^2  X X^2 X^2+X  0 X^2 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 69.

Homogenous weight enumerator: w(x)=1x^0+140x^69+240x^70+256x^71+263x^72+230x^73+187x^74+130x^75+131x^76+90x^77+54x^78+72x^79+81x^80+52x^81+48x^82+30x^83+11x^84+12x^85+6x^86+8x^87+1x^88+2x^89+1x^90+2x^93

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 0.382 seconds.