The generator matrix

 1  0  0  1  1  1  2  1  1  2  1  1  0  0  1  1  1  1  X X^2+X+2  1  1  0 X^2  X X+2  1  1  1  1 X^2+2  X  1  1 X+2 X^2+X+2  1  1  1 X^2+X  X  1 X^2+X X^2  0  1 X^2  1 X^2+2 X^2+X+2  1  1  X  1 X^2+X+2  1  1  1 X^2+2 X+2  2  1 X^2+X+2  1  1  1  1 X^2  1  1  1  1  1  1 X^2  1  X  1  1  1 X^2+2  1  1  1
 0  1  0  2 X^2+1 X^2+3  1  0 X^2+1  1  2 X^2+3  1 X^2+X X+2  X X^2+X+3 X^2+X+1 X^2+X+2 X^2+2 X^2+X+2 X+3  1  1  1  1 X^2+X+3 X^2+X X^2+1 X^2+2  1  0  1 X+2  1  1 X^2+X+1  1 X^2+2 X^2+X+2  1 X+1  1  X X^2+2  0  1  2  1  X X^2+X+2 X^2+3 X^2 X+3  1 X+3 X^2+X  2  1  1  1 X^2+X+1  1  X X^2+X X+3 X+2  1 X^2 X^2+X+2 X^2+X  3 X^2  3 X^2  2  1 X^2+X+2 X^2+X+3  0  1  X X^2+X+2  0
 0  0  1 X+3 X+1  2 X^2+X+1 X^2+X X^2+1  3 X^2+3 X^2+X+2 X^2+X+2  1 X^2+X X^2+3 X+1  2  1  1 X^2+X+3 X+2 X+2  3 X^2+1  X  3 X^2  3 X^2+X+2 X^2+X+3  1 X+3 X^2+2  0 X^2+3 X^2+X+1  0 X^2+2  1 X^2+X+2 X^2+1 X^2+X+1  1  1 X^2+2  X  X  2  1  X X+2  1 X^2+X  0  0 X^2+1 X^2+X+3 X+1 X^2+X+1 X^2+3 X^2+2  1 X+1 X^2+X+2 X^2+X+1  2 X^2+2  3  1 X+1 X^2+X X^2+X+3 X^2+2  1  3 X+2 X^2+2 X^2+X+2 X^2+3 X^2+3 X^2+X+1  2 X^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+166x^80+760x^81+588x^82+644x^83+460x^84+424x^85+280x^86+280x^87+103x^88+136x^89+68x^90+68x^91+50x^92+56x^93+8x^94+1x^96+2x^100+1x^104

The gray image is a code over GF(2) with n=672, k=12 and d=320.
This code was found by Heurico 1.16 in 0.421 seconds.