The generator matrix

 1  0  1  1  1 3X+2  1  1 2X+2  1  1  X  1  1 2X  1 X+2  1  1  2  1  1  1  0  1 3X  1  1  1 X+2 2X+2  1  1  1  1 3X  1 X+2  1  1  1 3X  1  1  2  1  1 2X  X  0  1 2X  1  1 2X+2 2X  1  0  1  1  1  1  1  1  1  1  1  1  1 3X+2  1 3X  1  1  1  1 3X+2  1  1  1  1 2X+2 3X+2  1
 0  1 X+1 3X+2  3  1 2X X+3  1 2X+2 2X+1  1  X X+1  1 2X+3  1 X+2  1  1  2 3X  3  1 3X+3  1 2X 3X+2 X+1  1  1 2X+1  2  X 3X+3  1 3X+1  1  2  X 3X+3  1 2X 2X+3  1 3X+2  1  1 3X  X 2X+3  1 2X+1 2X+3  1  1  3  1 2X+1 3X+1 2X+1 3X+1  3 3X+3 X+1 X+1 X+3 3X+3 2X+1  1 3X+1  1  2  X  0 X+2  1  X 3X 3X+3  2  1  1  0
 0  0  2  2 2X  2 2X+2 2X+2 2X 2X  0 2X+2 2X+2  0 2X+2  2 2X  0 2X+2  2  2 2X  0 2X 2X  0  2 2X+2 2X  0  0 2X 2X+2  2  0 2X 2X+2 2X+2  0  0  2  2 2X 2X+2 2X+2 2X  2  2 2X 2X 2X 2X 2X  0 2X  0 2X+2 2X+2  0 2X+2 2X+2  0  2  0 2X+2 2X  2 2X  2  2  2 2X  2  2 2X 2X 2X+2  0 2X+2  2  0  2 2X  0
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X  0  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X  0 2X  0 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X  0 2X 2X 2X 2X 2X 2X  0 2X  0  0  0 2X 2X 2X 2X  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+99x^80+340x^81+156x^82+444x^83+148x^84+290x^85+135x^86+252x^87+84x^88+80x^89+10x^90+1x^92+2x^93+1x^94+1x^98+2x^100+1x^114+1x^116

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 0.719 seconds.