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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+112x^82+54x^84+64x^86+5x^88+16x^90+1x^92+1x^96+1x^104+1x^108

The gray image is a code over GF(2) with n=336, k=8 and d=164.
This code was found by Heurico 1.16 in 0.496 seconds.