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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+32x^85+120x^86+16x^87+25x^88+10x^89+38x^90+4x^92+4x^93+1x^94+2x^97+2x^100+1x^102

The gray image is a code over GF(2) with n=348, k=8 and d=170.
This code was found by Heurico 1.16 in 1.17 seconds.