The generator matrix

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

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+167x^80+702x^81+970x^82+1196x^83+1158x^84+942x^85+693x^86+750x^87+462x^88+364x^89+247x^90+234x^91+129x^92+84x^93+52x^94+12x^95+17x^96+4x^97+5x^98+1x^100+1x^102+1x^104

The gray image is a code over GF(2) with n=680, k=13 and d=320.
This code was found by Heurico 1.16 in 1.22 seconds.