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

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+50x^80+80x^81+130x^82+184x^83+170x^84+168x^85+110x^86+72x^87+32x^88+8x^89+8x^90+2x^92+6x^94+2x^98+1x^128

The gray image is a code over GF(2) with n=672, k=10 and d=320.
This code was found by Heurico 1.16 in 0.687 seconds.