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

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

Homogenous weight enumerator: w(x)=1x^0+25x^84+4x^86+2x^90

The gray image is a code over GF(2) with n=656, k=5 and d=336.
This code was found by Heurico 1.16 in 0.344 seconds.