The generator matrix

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

generates a code of length 85 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+91x^80+314x^81+562x^82+514x^83+499x^84+516x^85+444x^86+300x^87+284x^88+226x^89+152x^90+90x^91+50x^92+12x^93+20x^94+2x^96+12x^97+4x^98+1x^100+1x^102+1x^118

The gray image is a code over GF(2) with n=680, k=12 and d=320.
This code was found by Heurico 1.16 in 0.922 seconds.