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

generates a code of length 82 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+28x^81+82x^82+6x^84+4x^86+4x^89+2x^98+1x^104

The gray image is a code over GF(2) with n=656, k=7 and d=324.
This code was found by Heurico 1.16 in 0.359 seconds.