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

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+392x^79+113x^80+468x^81+426x^82+336x^83+737x^84+400x^85+396x^86+352x^87+98x^88+212x^89+10x^90+96x^91+7x^92+24x^93+8x^95+3x^96+16x^97+1x^136

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 52 seconds.