The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  1  1  X  1  1  0  X  1
 0  X  0  X  2  2 X+2 X+2 X^2 X^2+X X^2 X^2+X+2 X^2+2 X^2+X X^2 X^2+X+2 X^2+2 X^2+X  2 X^2+X+2  2  X  X X^2 X^2+2  2  X  X X^2+X+2 X^2+2  0 X^2+X+2  X X+2 X^2+2 X^2  2  2 X^2+X X^2+X  0 X+2 X^2+X X^2+2  X X^2+X+2 X^2  2  0  2  X X^2+X X^2 X^2+X X^2+2 X^2+X+2 X^2+2  0 X^2+X+2 X+2 X+2 X^2+2  0 X+2 X+2 X^2+2  0 X+2 X+2 X^2+2 X+2 X+2 X+2  2 X^2+X+2 X^2+X  X X^2+X X+2  X X^2+X  2  2  2  0
 0  0  X  X X^2 X^2+X+2 X^2+X X^2+2 X^2 X^2+X  X X^2+2 X^2+X+2  0  2 X+2  X  0 X^2+2 X^2+X+2  0 X^2+X  2 X^2+X X^2 X^2+X X^2  X X+2  0 X+2 X^2+2 X^2+X+2  0 X^2+X+2  2  2  X X^2+X+2 X^2+2 X^2+2 X+2  2 X+2 X^2+2  X X^2+2 X^2+X  X  2 X^2 X+2 X^2+X X^2+X+2  2  2 X^2 X^2+X+2 X^2 X^2+X+2 X+2 X+2 X^2+2  2 X^2 X^2+X  2  X X^2+X+2  X  X X^2+2 X^2+X X^2+2 X^2+X+2  0  X X^2+2  0 X^2+2  X X^2  X  X  2
 0  0  0  2  2  2  0  2  0  2  2  0  0  2  2  0  0  0  0  0  2  2  2  2  2  0  0  0  2  0  2  2  0  2  2  0  2  0  2  0  0  2  2  0  0  0  2  2  2  0  2  2  0  0  2  0  0  0  2  2  0  2  2  0  2  0  0  2  0  2  0  0  2  2  2  2  0  2  0  0  0  0  0  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+142x^81+133x^82+194x^83+313x^84+522x^85+346x^86+160x^87+68x^88+86x^89+33x^90+46x^91+1x^92+2x^93+1x^160

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 0.766 seconds.