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  X  0  X  0  X  0  X  0  X  X  X  X  X  X  2  X  X  2  X  2  X  2  1  1  1  1  2  2  2  2  0  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  0
 0  X  0 X+2  0 X+2  0  X  0 X+2  0  X  0 X+2  0  X  2 X+2  2  X  2 X+2  2  X  2 X+2  2  X  2 X+2  2  X X+2  X X+2  X X+2  X X+2  X  0  0  0  2  2  X  X  2  X  X  X  X  X  X  0  0  2  2  0  0  0  2  2  2 X+2 X+2  X  X  0  0  2  2 X+2 X+2  X  X  0  0 X+2  2  0  2 X+2  0  2
 0  0  2  0  0  0  2  0  0  2  0  2  2  2  2  2  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  2  0  0  0  0  2  2  2  2  0  2  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  2  0  0  2
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  2  2  0  0  2  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  0  0  2  2  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  0  2  0  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  2  0  0  0  2  2  0  2  0  0  2  0  2  2  0  0  2  2  0  2  0  2  2  0  2  0  2  0  2  2  0  0  2  0  2  2  0  0  2  0  0  0  2  0  2  2  0  2  0  0  2  0  2  2  0  0  2  2  0  2  0  0  0  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+63x^82+69x^84+61x^86+55x^88+1x^90+3x^94+1x^108+2x^116

The gray image is a code over GF(2) with n=340, k=8 and d=164.
This code was found by Heurico 1.16 in 0.44 seconds.