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

generates a code of length 83 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+36x^82+64x^83+12x^84+8x^86+4x^90+1x^96+2x^104

The gray image is a code over GF(2) with n=664, k=7 and d=328.
This code was found by Heurico 1.16 in 0.375 seconds.