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

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+57x^84+158x^86+27x^88+10x^92+1x^108+2x^118

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 0.346 seconds.