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  0  X 2X+2  X  0  X 2X+2  X  0  X 2X+2  X  X  0  2 2X+2  2  X  1
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 X+2 3X 2X+2  0 X+2 2X+2  X  0 X+2 2X+2 3X  0 X+2 2X+2 3X 2X 3X+2  2 3X 2X 3X+2  2 3X  0 X+2 2X+2  X 2X 3X+2  2 3X 3X+2 2X  2  X 2X X+2  2  X 3X+2  0  X 2X+2 2X  X  2 3X+2 2X  X  2 3X+2 2X 3X+2  2 3X X+2  X 3X  X X+2  X 3X  X X+2  X 3X  X X+2 3X+2  X  0  X  0 3X+2  0
 0  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X  0 2X  0  0 2X  0  0 2X  0  0  0 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X  0  0  0
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X  0 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X  0 2X  0  0  0  0  0
 0  0  0  0 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0  0  0  0  0  0  0 2X  0 2X  0  0 2X  0  0 2X 2X 2X  0 2X  0 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X 2X  0  0  0 2X  0  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+23x^80+84x^81+254x^82+140x^83+103x^84+48x^85+288x^86+16x^87+16x^88+28x^89+16x^90+4x^91+1x^98+1x^100+1x^130

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.