The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^82+2x^84+8x^86+3x^88+1x^92+1x^100

The gray image is a code over GF(2) with n=328, k=6 and d=164.
This code was found by Heurico 1.16 in 0.184 seconds.