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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+32x^68+44x^69+80x^70+138x^71+153x^72+152x^73+173x^74+216x^75+207x^76+194x^77+170x^78+130x^79+78x^80+70x^81+57x^82+36x^83+23x^84+18x^85+29x^86+18x^87+16x^88+2x^89+2x^90+4x^91+2x^92+2x^95+1x^126

The gray image is a linear code over GF(2) with n=304, k=11 and d=136.
This code was found by Heurico 1.16 in 0.55 seconds.