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  1  1  1  1  1  1  1  2  1  1  1  1  0  1  1  1  1  2  1  2
 0 2X+2  0  0  0  2 2X+2  2  0  0  0  0  2 2X+2  2 2X+2  0 2X  2 2X+2 2X  0 2X+2  2  0 2X 2X 2X+2 2X+2  2 2X  2  2 2X 2X  0  0  2  2 2X+2  0 2X  2 2X 2X  2  2 2X+2  2  0 2X 2X+2  0  2 2X  0 2X+2  2 2X  2 2X+2  0 2X+2  2 2X 2X+2 2X+2  2 2X  0 2X+2 2X+2  2 2X+2 2X+2 2X+2  2  2 2X  2  2 2X+2  0 2X+2
 0  0 2X+2  0  2  2 2X+2  0  2  0  0 2X+2  2 2X+2  0  0  0 2X+2 2X+2 2X  0 2X+2 2X+2 2X 2X 2X+2 2X+2  0 2X  2  0  2 2X  0 2X+2  2 2X 2X+2  0 2X+2  0  2 2X+2 2X  2 2X 2X  2  0 2X 2X+2 2X+2  2 2X 2X+2 2X 2X  2  0  0  2 2X+2  2  0 2X 2X  2  2 2X  0 2X+2  2 2X+2 2X  0 2X 2X+2  0 2X  0 2X  2  0  2
 0  0  0 2X+2  2  0 2X+2  2  2  0 2X+2  0  0 2X+2  2  0 2X  2  2  0  2 2X  0  2 2X 2X+2  0  2 2X  2 2X+2 2X  0 2X 2X+2 2X 2X+2  2 2X+2 2X  2  2  0  0 2X 2X+2 2X  2  0  0 2X  0 2X+2 2X+2 2X  0  2 2X+2 2X+2 2X 2X  2  2  0  2 2X 2X+2  2 2X+2  2  2 2X+2 2X+2  2 2X+2  0 2X+2 2X 2X+2 2X+2  2 2X+2  2  2
 0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X  0 2X  0 2X 2X  0  0  0  0 2X 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0  0 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X  0 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+270x^80+128x^81+128x^82+384x^83+256x^84+384x^85+128x^86+128x^87+224x^88+16x^96+1x^160

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 113 seconds.