The generator matrix

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

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+68x^81+284x^82+322x^83+249x^84+358x^85+148x^86+262x^87+211x^88+54x^89+62x^90+20x^91+2x^92+1x^94+2x^95+2x^103+1x^118+1x^124

The gray image is a code over GF(2) with n=680, k=11 and d=324.
This code was found by Heurico 1.16 in 0.735 seconds.