The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+58x^83+50x^84+48x^85+154x^86+132x^87+44x^88+4x^90+18x^91+1x^104+1x^114+1x^122

The gray image is a code over GF(2) with n=344, k=9 and d=166.
This code was found by Heurico 1.16 in 3.11 seconds.