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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+54x^84+100x^85+24x^86+34x^88+24x^89+2x^90+4x^92+4x^93+4x^94+1x^96+2x^98+2x^100

The gray image is a code over GF(2) with n=344, k=8 and d=168.
This code was found by Heurico 1.16 in 0.34 seconds.