The generator matrix

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

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+737x^80+874x^82+981x^84+796x^86+635x^88+26x^90+27x^92+16x^96+3x^112

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 64.3 seconds.