The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+75x^68+112x^69+174x^70+408x^71+342x^72+836x^73+585x^74+1242x^75+833x^76+1704x^77+1103x^78+1750x^79+1077x^80+1562x^81+842x^82+1374x^83+554x^84+758x^85+282x^86+294x^87+140x^88+118x^89+57x^90+48x^91+41x^92+26x^93+23x^94+4x^95+8x^96+4x^97+4x^98+1x^100+2x^102

The gray image is a linear code over GF(2) with n=316, k=14 and d=136.
This code was found by Heurico 1.16 in 20.1 seconds.