The generator matrix

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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+67x^68+174x^69+207x^70+212x^71+192x^72+190x^73+173x^74+138x^75+161x^76+118x^77+92x^78+138x^79+81x^80+22x^81+30x^82+16x^83+5x^84+6x^85+6x^86+6x^87+4x^88+3x^90+2x^91+2x^93+1x^94+1x^100

The gray image is a linear code over GF(2) with n=296, k=11 and d=136.
This code was found by Heurico 1.16 in 0.491 seconds.