The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1 X+2  1  1 3X  1  1 2X+2  1 2X  1  1  2  1  1 X+2  1  1  1 3X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 3X+2  X 2X+2  0 X+2 2X+2 3X  0 2X X+2 3X+2 2X+2  2  1  1  2  X 3X  1
 0  1 X+1 X+2  3  1 3X+3 2X+2  1 3X 2X+1  1  0 X+1  1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+1  1 X+2  3  1 3X 3X+3  1 2X+1 2X+2  1 2X  1 X+1 X+2  1 3X+3  3  1  2 3X 2X+1  1 3X+2  0  X 2X+2  0 X+2 2X+2 3X  0 X+2 2X+2 3X 2X 3X+2  2  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1 3X+1 X+3 2X+2  1  1 3X+1
 0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X 2X 2X  0  0 2X  0  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X 2X 2X 2X  0 2X
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X  0 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0  0
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0 2X  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0 2X  0  0  0  0  0 2X 2X 2X  0 2X 2X  0 2X 2X 2X  0 2X  0 2X 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+260x^80+132x^81+124x^82+228x^83+540x^84+340x^85+62x^86+28x^87+286x^88+40x^89+4x^90+2x^102+1x^128

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 0.468 seconds.