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

generates a code of length 86 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+513x^82+448x^83+580x^84+412x^85+468x^86+364x^87+408x^88+340x^89+337x^90+100x^91+68x^92+30x^94+8x^96+12x^98+4x^100+1x^108+1x^112+1x^116

The gray image is a code over GF(2) with n=688, k=12 and d=328.
This code was found by Heurico 1.16 in 33.7 seconds.