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

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+3x^86+22x^87+3x^88+1x^94+2x^95

The gray image is a code over GF(2) with n=340, k=5 and d=172.
This code was found by Heurico 1.16 in 0.319 seconds.