The generator matrix

 1  0  1  1  1 X^2+X+2  X  1  1  2  1  1 X^2  1  1  1 X^2+X  1  1 X^2+2  1 X+2  1  1  1  1  1 X+2  1  0  1  1 X^2+2  1 X^2+X+2  1  1  1  1  2  1 X^2+X  1 X^2  1  X  1  1  1  X X^2  1 X+2  2  1  1  X  1 X^2+X  1  1  1  1  1  1  1  1 X^2  1  1  1  1  1  1  1  1  X  X  X  1  1  1  0  1
 0  1 X+1 X^2+X X^2+3  1  1 X^2+2 X^2+X+1  1 X+2  1  1  2 X+1 X^2+X+2  1 X^2+X+3 X^2  1  X  1 X+1 X^2+X+3 X^2+1  3  0  1 X^2+1  1 X^2+X+2 X+3  1  3  1  2  X X^2+X+3 X^2  1  X  1 X^2+3  1  1  1 X^2+X X^2+X+2  1  X  1 X^2+2  1  1 X+1 X^2 X^2+X+2  3  1 X+1 X^2+1 X+1 X^2+X+1 X^2+3 X+1  X  3  X X^2+3 X^2+X+1 X^2+3 X+3 X^2+3 X^2+X+2 X^2+X+3 X^2+2  1  1  1 X^2 X^2+X+3 X^2+2  1 X+1
 0  0 X^2  0 X^2+2 X^2 X^2  0 X^2+2 X^2+2  0 X^2 X^2+2 X^2  2 X^2+2  0  2 X^2  0 X^2+2  0  2  2  0  2  0  0  2  0 X^2+2 X^2  0  2 X^2+2 X^2+2  0 X^2+2 X^2 X^2 X^2  2 X^2 X^2+2 X^2+2 X^2  0  2  0  2  2  2 X^2+2  0  2  0 X^2 X^2+2 X^2 X^2+2 X^2+2 X^2  0  2 X^2+2 X^2 X^2 X^2+2  0  2 X^2+2  0  2 X^2  0 X^2  2 X^2+2 X^2+2  2  0  2 X^2  2
 0  0  0  2  0  0  0  0  2  2  2  2  2  0  2  2  2  0  2  2  0  0  2  0  0  2  2  0  2  0  2  0  2  0  2  2  2  2  0  0  0  2  0  0  2  2  0  0  2  2  0  2  2  2  0  0  0  0  0  2  0  2  2  0  2  2  0  0  0  2  2  0  0  0  2  0  2  2  0  0  0  2  2  0
 0  0  0  0  2  0  2  2  0  0  2  2  2  2  0  2  0  0  0  2  0  2  2  2  0  2  2  0  0  2  0  2  0  2  2  2  0  2  0  2  2  2  0  0  0  0  2  0  0  0  2  0  2  2  0  0  0  2  2  2  0  0  2  0  0  0  0  2  2  2  2  0  2  0  0  2  0  0  0  2  2  2  2  2

generates a code of length 84 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+144x^79+281x^80+560x^81+396x^82+546x^83+445x^84+458x^85+443x^86+348x^87+172x^88+184x^89+39x^90+48x^91+8x^92+10x^93+1x^94+2x^96+2x^99+2x^100+4x^101+1x^114+1x^116

The gray image is a code over GF(2) with n=672, k=12 and d=316.
This code was found by Heurico 1.16 in 0.906 seconds.