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

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

Homogenous weight enumerator: w(x)=1x^0+24x^82+200x^84+24x^86+2x^88+1x^96+4x^100

The gray image is a code over GF(2) with n=672, k=8 and d=328.
This code was found by Heurico 1.16 in 0.641 seconds.