The generator matrix

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

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+112x^81+158x^82+188x^83+124x^84+112x^85+51x^86+48x^87+45x^88+28x^89+25x^90+56x^91+36x^92+24x^93+5x^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 1.16 in 1.98 seconds.