The generator matrix

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

generates a code of length 85 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+164x^79+753x^80+1244x^81+1731x^82+1884x^83+2282x^84+1674x^85+1672x^86+1332x^87+1329x^88+878x^89+621x^90+304x^91+186x^92+166x^93+99x^94+20x^95+20x^96+6x^97+4x^98+4x^99+4x^100+1x^102+4x^103+1x^104

The gray image is a code over GF(2) with n=680, k=14 and d=316.
This code was found by Heurico 1.16 in 4.02 seconds.