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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+103x^68+270x^70+32x^71+359x^72+144x^73+401x^74+236x^75+502x^76+240x^77+469x^78+204x^79+332x^80+112x^81+239x^82+36x^83+153x^84+16x^85+109x^86+4x^87+70x^88+44x^90+13x^92+4x^94+2x^96+1x^116

The gray image is a linear code over GF(2) with n=308, k=12 and d=136.
This code was found by Heurico 1.16 in 1.83 seconds.