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

generates a code of length 84 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+254x^80+128x^81+152x^82+256x^83+296x^84+640x^85+48x^86+208x^88+56x^90+8x^92+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 1.47 seconds.