The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  X  X  X  1  1  1  1  1  1  1  X  X  X  X  X  X  X  1  1  1  1  1  2  2  2  2  2  2  2  X  0  0  0  0  0  0  0  X  1  X  X  X  X  X  X  X  1  1  1  1  1  X  2  1
 0  2  0  0  0  2  2  2  0  0  0  2  0  2  2  2  0  0  0  2  0  2  2  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  2  2  2  2  0  0  0  0  0  0  2  0  2  0  2  2  0  0  2  0  2  0  0  2
 0  0  2  0  2  2  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  0  0  2  0  2  2  2  2  0  0  0  0  2  2  2  0  0  0  2  2  2  2  2  0  0  0  2  2  0  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  0  0  2  2  2  2  0  0  0
 0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  2  2  0  0  0  2  2  0  2  2  0  0  0  2  2  0  0  2  2  0  0  2  2  2  0  2  0  0  0  0  2  2  2  2  0  0  2  0  0  2

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

Homogenous weight enumerator: w(x)=1x^0+7x^86+46x^87+7x^88+1x^94+2x^95

The gray image is a code over GF(2) with n=344, k=6 and d=172.
This code was found by Heurico 1.16 in 0.335 seconds.