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

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

Homogenous weight enumerator: w(x)=1x^0+66x^81+20x^82+14x^83+6x^84+6x^85+4x^86+2x^87+8x^89+1x^104

The gray image is a code over GF(2) with n=328, k=7 and d=162.
This code was found by Heurico 1.16 in 0.528 seconds.