The generator matrix

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

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+124x^68+468x^69+983x^70+1356x^71+2042x^72+2648x^73+3392x^74+3924x^75+4410x^76+5144x^77+5367x^78+5556x^79+5457x^80+5376x^81+4727x^82+4036x^83+3332x^84+2548x^85+1840x^86+1136x^87+714x^88+424x^89+267x^90+120x^91+66x^92+32x^93+26x^94+14x^96+6x^98

The gray image is a linear code over GF(2) with n=316, k=16 and d=136.
This code was found by Heurico 1.13 in 65.1 seconds.