The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X 2X+2  X  0  X 2X+2  X  0  X 2X+2  X  0  X 2X  2  X 2X  2  X  X
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 X+2 3X 2X+2  0 X+2 2X+2  X  0 X+2 2X+2 3X  0 X+2 2X+2  X  0 3X+2  2 3X 2X 3X+2  2  X 2X X+2 2X+2  X 2X 3X+2  2 3X 2X 3X+2  2 3X 2X 3X+2  2 3X  0 X+2 2X+2 3X 2X 3X+2  2  X 2X 3X+2  2  X 2X 3X+2  2  X X+2  X 3X  X X+2  X 3X  X X+2  X 3X  X X+2  X 3X+2  X  0 3X+2  X  0  0  0
 0  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0 2X  0  0 2X  0 2X 2X  0  0  0 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X  0 2X 2X  0  0  0 2X  0  0
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0 2X 2X 2X  0  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0  0  0 2X 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0  0 2X  0
 0  0  0  0 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0  0  0  0  0 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X 2X  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+34x^82+72x^83+218x^84+120x^85+156x^86+96x^87+226x^88+64x^89+2x^90+24x^91+8x^93+2x^100+1x^128

The gray image is a code over GF(2) with n=688, k=10 and d=328.
This code was found by Heurico 1.16 in 0.719 seconds.