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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+68x^67+105x^68+162x^69+126x^70+262x^71+142x^72+488x^73+120x^74+608x^75+118x^76+594x^77+98x^78+418x^79+111x^80+230x^81+46x^82+134x^83+82x^84+40x^85+40x^86+40x^87+10x^88+18x^89+18x^90+6x^91+6x^92+4x^93+1x^116

The gray image is a linear code over GF(2) with n=304, k=12 and d=134.
This code was found by Heurico 1.16 in 10.6 seconds.