The generator matrix

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

generates a code of length 85 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+116x^81+710x^82+748x^83+698x^84+444x^85+318x^86+252x^87+186x^88+176x^89+185x^90+104x^91+96x^92+16x^93+42x^94+2x^96+1x^104+1x^106

The gray image is a code over GF(2) with n=680, k=12 and d=324.
This code was found by Heurico 1.16 in 0.438 seconds.