The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1 X^2+X  1  1  0  1  0  1  1 X^2+X  1  1  1  0  1  1 X^2  1  1 X^2+X  1  1  1  1  1  1  1 X^2+X  1  1 X^2  1  1  1 X^2+X  1  1  1  1 X^2+X  1  X  1  1  1  0  0  1  1  1  X  1  1  1  1  0  1 X^2+X  1  1  0  X X^2  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1 X^2+1  1 X^2+X X+1  1  0  0 X+1  1 X^2+X X^2+1  1  1  0  1  X X^2+X+1 X^2+X X^2 X^2+1  0 X+1  1  0 X^2+X  1 X+1 X^2+X+1 X^2+X+1  1 X^2  X X^2+1 X^2+X  1 X^2+X  1 X^2+X  X X+1  1  1 X+1 X^2+X+1 X^2+1  0 X^2 X^2+X X^2 X^2+X  1 X^2+1  1 X+1 X^2+X+1  X  1  X  0
 0  0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  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 X^2 X^2 X^2  0  0  0  0
 0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2  0
 0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2
 0  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 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 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+34x^68+58x^69+124x^70+224x^71+179x^72+332x^73+216x^74+444x^75+212x^76+468x^77+267x^78+404x^79+233x^80+368x^81+122x^82+196x^83+86x^84+50x^85+22x^86+12x^87+13x^88+4x^89+5x^90+4x^92+3x^94+6x^96+8x^98+1x^106

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 1.32 seconds.