The generator matrix

 1  0  0  1  1  1 X^2 X^3  0 X^3+X^2  1  1  1  1  X  1 X^3+X^2+X  1  1  1 X^2+X X^3+X^2+X  1  1 X^3+X^2+X X^3+X^2+X  1  1  1 X^2+X X^3+X^2  1  0  1  1  1  1 X^3+X^2+X X^3+X^2+X  X  1  1  1 X^2  1 X^3+X  1 X^2  X X^2  1 X^3+X  1 X^3 X^3+X  1  1  1  1  0  0  1  1 X^3  1 X^2  1  1 X^3+X  1  1  1  1 X^3 X^3+X^2+X X^3+X X^3+X^2 X^3  0  1 X^3+X^2+X X^2  1 X^2+X  1
 0  1  0  0 X^3+X^2+1 X^3+X^2+1  1 X^2+X  1  1  0 X^3 X^3+X^2+1 X^2+1  X  X  1 X^3+X+1 X^2+X X^3+X+1  1  1 X+1 X^3+X^2+X X^3+X^2  1 X^2+X X^3+X^2+X+1  1 X^3+X  1  0  1 X^2+X+1 X^3+X^2 X^3+X^2 X+1  1  1  1 X^3+X^2+X+1 X^3 X^3+1 X^3+X X^2+X  1 X+1  1  1  1 X^3+X^2 X^2 X^2+X  1  1 X^3+X X^3+X X^2+X+1 X^2  1 X^2+X  X X^3+X^2+X  1 X^3 X^2 X^2+X+1 X+1  1 X^2+X  X X^3 X^2+X X^2+X X^3 X^3 X^2 X^2  1 X^2+X  X X^3+X^2 X^2+1  1 X^3
 0  0  1 X+1 X^3+X+1 X^2 X+1  1 X^3+X^2+X X^3+1 X^2+1 X^2+X X^3+1  X  1  1 X^3+1 X^3+X^2+X+1 X^3+X^2+X  X X^2+X X^2 X^3 X^3+X^2+X+1  1 X^3+X^2+X+1 X^3 X^3+1  X  1 X^3+X X^3+X X^3+X+1 X^2+X+1 X^3+1 X^3 X^2+X X^3+X X+1  1  0 X^3+X+1 X^3+X^2+X+1  1 X^3+X^2+1 X^2 X^3 X^3+X+1 X^2+X X^3+1 X^2  1 X^3+X^2+X+1  X X^3+X^2 X^3+X^2+1 X^2+X X^3+X^2+1 X+1 X^2+X+1  1 X^3 X^3+X^2 X^3+X^2+1 X^2+X+1  1 X^3+X+1 X^3+1 X^3+X^2+1 X^3+X+1 X^3+X^2+X  1 X^3+1  1  1  1  1  1 X^2+X X^3+X  1  1 X^2+1 X+1  0
 0  0  0 X^2 X^2  0 X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^3  0  0  0 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2  0  0 X^3+X^2 X^3+X^2  0 X^2 X^3 X^2  0 X^3+X^2 X^2 X^3 X^3 X^2 X^2 X^2  0 X^3 X^3 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2  0 X^2  0 X^3  0  0 X^3 X^3 X^3+X^2  0 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3 X^2 X^3  0 X^3+X^2  0 X^3  0  0 X^3 X^3 X^3 X^3+X^2

generates a code of length 85 over Z2[X]/(X^4) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+134x^79+909x^80+1304x^81+1581x^82+1812x^83+2034x^84+1794x^85+1887x^86+1384x^87+1158x^88+900x^89+647x^90+336x^91+254x^92+110x^93+84x^94+22x^95+8x^96+4x^97+7x^98+8x^99+4x^100+1x^102+1x^106

The gray image is a linear code over GF(2) with n=680, k=14 and d=316.
This code was found by Heurico 1.16 in 5.81 seconds.