The generator matrix

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

generates a code of length 84 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+398x^81+214x^82+492x^83+84x^84+304x^85+200x^86+212x^87+10x^88+106x^89+16x^91+8x^97+2x^98+1x^128

The gray image is a code over GF(2) with n=672, k=11 and d=324.
This code was found by Heurico 1.16 in 2.09 seconds.