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 X^2  X  1  X  1 X^2  X  X  X  1 X^2  X  X  1  2 X^2  0  X X^2  X X^2  X  2 X^2  0 X^2  2  X X^2  X  2 X^2  X  X  X
 0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  2  0  2  0  2  2  0  2  2  0  2  2  0  2  2  0  0  0  2  2  0  2  2  0  0  2  2  0  2  0  0  2  2  0  2  2  0  2  0  2  2  0  0  2  0  2  2  0  0  0  2  0  0  0  2  0

generates a code of length 82 over Z4[X]/(X^3+2,2X) 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 0.36 seconds.