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  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  X  2  1
 0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X  2 2X+2  0 2X+2  0 2X+2  0 2X+2  2  0 2X 2X+2  0 2X 2X+2  2 2X+2 2X 2X+2  0  0
 0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0  0  0 2X 2X  0  0 2X 2X 2X  0 2X  0 2X  0 2X  0
 0  0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  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 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0 2X  0 2X  0 2X 2X 2X  0  0 2X  0  0 2X 2X 2X  0
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X 2X  0 2X 2X  0  0 2X  0  0  0  0 2X  0 2X  0
 0  0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0  0 2X 2X  0 2X  0  0 2X 2X  0  0  0  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+36x^80+16x^81+100x^82+176x^83+386x^84+176x^85+80x^86+16x^87+18x^88+12x^90+6x^92+1x^160

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 0.671 seconds.