The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2) 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.