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

generates a code of length 84 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+214x^80+472x^82+552x^84+512x^85+48x^86+168x^88+56x^90+24x^92+1x^160

The gray image is a code over GF(2) with n=672, k=11 and d=320.
This code was found by Heurico 1.16 in 6.72 seconds.