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  2  1  1  1  1  2  1  1  X  1  1 X^2+X+2  1  1  0  1 X+2  1  1 X^2+X+2 X+2  1 X^2  1  1  0  1  1  1  1  1 X^2+X+2  1 X^2+2 X^2+X+2  2  1  1 X^2+2 X+2 X^2 X^2+X+2  1  1  1  1  X  1  1 X^2+X X+2  0 X^2  2  1 X^2+X X^2+X  1 X+2  0  1  1  X  1  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 X+1 X^2+X X+3  1 X^2 X^2+1  1 X^2+X+3 X^2+2  1  1  X  1 X^2+3  1 X+2 X+1  1  1 X^2  1  3 X+2  1 X^2+2  2 X^2+X+1 X^2+X X+1  1 X^2+X  X  1  1  X X^2+X+2  1  1  1  1 X+2 X^2+X+1 X^2+1  2  1 X^2 X+3  1  1  1  1  1 X^2+1  1  1  3  1  1 X^2+X+3  3  1 X+3  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 X^2 X^2+X X^2+X X^2 X^2 X^2 X^2+X  X X^2+2 X^2+X  2 X^2 X^2+X+2  2  0 X^2+X+2  2 X+2 X^2+X X^2+2 X^2+2 X^2+X X^2+X  X X^2+2  0  X  0 X^2+2 X^2+X X^2+X+2  0 X^2+2  X X^2+X+2 X^2+2 X^2+X  0  2 X^2+2 X^2  X  0  X  0 X+2 X^2+X+2 X^2+X+2 X+2  2 X+2 X+2 X^2+2 X^2 X^2 X^2+2  X X^2+X X^2 X^2 X+2  2  0 X+2
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  2  2  0  0  0  2  2  0  2  0  0  0  2  2  0  2  0  2  0  0  0  2  2  2  2  2  0  2  2  0  2  0  2  0  0  0  2  0  2  2  0  0  0  2  2  2  2  0  0  0  0  2  0  0  2  2  0  2  2  2  2  2  2  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+568x^79+212x^80+800x^81+186x^82+756x^83+176x^84+680x^85+164x^86+420x^87+20x^88+48x^89+2x^90+28x^91+2x^92+8x^93+20x^95+3x^96+2x^116

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 47.8 seconds.