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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+68x^82+38x^84+12x^86+8x^90+1x^104

The gray image is a code over GF(2) with n=332, k=7 and d=164.
This code was found by Heurico 1.16 in 0.583 seconds.