The generator matrix

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

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+47x^68+88x^69+194x^70+286x^71+336x^72+334x^73+342x^74+340x^75+316x^76+368x^77+290x^78+304x^79+262x^80+202x^81+161x^82+80x^83+51x^84+18x^85+20x^86+10x^87+8x^88+8x^89+7x^90+4x^91+2x^92+6x^93+8x^94+1x^96+1x^98+1x^106

The gray image is a linear code over GF(2) with n=304, k=12 and d=136.
This code was found by Heurico 1.16 in 1.3 seconds.