The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+126x^81+157x^82+176x^83+130x^84+102x^85+51x^86+54x^87+39x^88+28x^89+14x^90+54x^91+52x^92+28x^93+1x^94+4x^95+4x^97+1x^104+1x^106+1x^120

The gray image is a code over GF(2) with n=340, k=10 and d=162.
This code was found by Heurico 1.11 in 12.7 seconds.