The generator matrix

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

generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+175x^68+176x^69+316x^70+188x^71+226x^72+168x^73+222x^74+92x^75+145x^76+68x^77+82x^78+20x^79+47x^80+32x^81+26x^82+20x^83+24x^84+4x^85+10x^86+5x^88+1x^96

The gray image is a linear code over GF(2) with n=292, k=11 and d=136.
This code was found by Heurico 1.16 in 0.371 seconds.