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  0  2  0  2  0  0  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  0  X  X  2  X  0  X  X  X  X  2  0  0  2  X
 0  X  0  0  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  X  X  0  X  0  X  2  2  2  2  2  2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2 X+2  2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2  X  X  X  X  X  2  X  2  2  X  2  X  0  X  X  0
 0  0  X  0  X  X  X  0  0  0  X  X  X  X  0  0  2  2 X+2 X+2 X+2 X+2  2  2  2  2 X+2 X+2 X+2  2 X+2  2  X  X  2  X  X  0  2 X+2  0  X X+2  2  X  0  2  X  2 X+2 X+2  2 X+2  2  X  0  X X+2  2  0  X  0  X  X  0  0  0 X+2 X+2  2  X  X  0  2 X+2 X+2  0  X  0  2  2  X  X X+2  X  0
 0  0  0  X  X  0  X  X  2 X+2 X+2  2  2 X+2 X+2  2  2  X X+2  0  2  X X+2  0  0 X+2  0 X+2  X  X  2  2  2 X+2  X  0  X  X  0  0  X  X  X  X  0  0  2  2  X X+2  0 X+2 X+2  2 X+2  2  X  2 X+2 X+2  2  2 X+2  0  0  X X+2  X  2  0  0  X X+2  2  2  X X+2  2 X+2 X+2  0  2  0  0  0  0

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+32x^82+92x^83+70x^84+48x^85+74x^86+56x^87+40x^88+16x^89+12x^90+44x^91+14x^92+10x^94+2x^96+1x^128

The gray image is a code over GF(2) with n=344, k=9 and d=164.
This code was found by Heurico 1.16 in 0.363 seconds.