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

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

Homogenous weight enumerator: w(x)=1x^0+62x^80+64x^81+278x^82+64x^83+24x^84+8x^86+8x^88+1x^96+2x^114

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 0.578 seconds.