The generator matrix

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

generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+132x^68+16x^69+232x^70+64x^71+222x^72+92x^73+246x^74+148x^75+235x^76+136x^77+146x^78+40x^79+138x^80+12x^81+74x^82+4x^83+59x^84+30x^86+10x^88+8x^90+2x^92+1x^120

The gray image is a linear code over GF(2) with n=300, k=11 and d=136.
This code was found by Heurico 1.16 in 0.566 seconds.