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

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+386x^81+265x^82+442x^83+89x^84+308x^85+181x^86+244x^87+21x^88+62x^89+16x^90+22x^91+1x^92+4x^95+4x^97+1x^106+1x^126

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 1.36 seconds.