The generator matrix

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

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+61x^82+48x^83+136x^84+32x^85+130x^86+48x^87+48x^88+1x^90+4x^96+1x^100+1x^116+1x^120

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 0.447 seconds.