The generator matrix

 1  0  1  1  1 3X+2  1  1 3X  1  1  2  1  1  2  1  1 3X  1  1 3X+2  1  1  0  1  1 2X  1  1 X+2  1  1  X  1  1 2X+2  1  1  1  1 2X X+2  1  1  1  1 2X+2  X  X  X  0  X  X  2  1  1  1  1  X  X  0  1  1  X  X  2  2  2  X 2X+2  1 3X  X  1  X  X 2X 3X+2 2X+2  1  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1 2X 3X+1  1 X+2  3  1 2X+2 3X+3  1  X  1  1 2X X+2 3X+1  3  1  1 2X+2  X 3X+3  1  1  1  0 3X+2  X  2 3X  X  0 2X 3X+2 X+2 2X 3X+2  X X+3 X+3 2X+2 3X  X  1  1  X  X 2X+1  1 X+2 2X+3  X X+2  X  1  X X+1 2X+1 X+1
 0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0 2X  0 2X 2X 2X 2X  0  0  0  0  0 2X 2X 2X  0  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0  0  0 2X  0  0  0  0 2X 2X 2X  0  0  0 2X  0 2X  0 2X  0  0 2X  0

generates a code of length 82 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+81x^80+124x^81+138x^82+76x^83+46x^84+16x^85+22x^86+4x^87+4x^93

The gray image is a code over GF(2) with n=656, k=9 and d=320.
This code was found by Heurico 1.16 in 0.375 seconds.