The generator matrix

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

generates a code of length 83 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+182x^79+660x^80+656x^81+688x^82+532x^83+324x^84+236x^85+208x^86+198x^87+164x^88+76x^89+110x^90+40x^91+17x^92+2x^94+1x^100+1x^104

The gray image is a code over GF(2) with n=664, k=12 and d=316.
This code was found by Heurico 1.16 in 0.422 seconds.