The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+507x^82+328x^83+822x^84+288x^85+592x^86+256x^87+491x^88+192x^89+357x^90+88x^91+106x^92+34x^94+13x^96+10x^98+4x^100+4x^102+2x^108+1x^112

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 6.17 seconds.