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

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

Homogenous weight enumerator: w(x)=1x^0+72x^82+128x^83+38x^84+12x^86+4x^98+1x^104

The gray image is a code over GF(2) with n=664, k=8 and d=328.
This code was found by Heurico 1.16 in 3.67 seconds.