The generator matrix

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

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+176x^82+662x^83+750x^84+608x^85+404x^86+452x^87+214x^88+332x^89+112x^90+110x^91+124x^92+44x^93+50x^94+32x^95+20x^96+2x^98+2x^100+1x^104

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 0.453 seconds.