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

generates a code of length 81 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+20x^83+5x^84+4x^85+2x^86

The gray image is a code over GF(2) with n=648, k=5 and d=332.
This code was found by Heurico 1.16 in 0.343 seconds.