The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+24x^82+152x^83+90x^84+86x^85+45x^86+38x^87+19x^88+30x^89+4x^90+2x^91+12x^93+2x^94+4x^98+1x^102+2x^104

The gray image is a code over GF(2) with n=340, k=9 and d=164.
This code was found by Heurico 1.16 in 0.227 seconds.