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  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  0  X  0  2  2
 0  X  0 X+2  0 X+2  0  X  0 X+2  0  X  0 X+2  0  X  0 X+2  0  X  0 X+2  0  X  0 X+2  0  X  0 X+2  0  X  2 X+2  2  X  2 X+2  2  X  2 X+2  2  X  2 X+2  2 X+2  2 X+2  2  X  2  X  2  X  2 X+2  2  X  2 X+2  2  X  0 X+2  0 X+2  0 X+2  2  X  0 X+2  0  0 X+2 X+2 X+2  2  X  X X+2  X  2  0
 0  0  2  0  0  0  2  0  0  0  0  0  2  0  2  0  0  2  0  2  0  2  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  2  0  2  0  0  0  2  0  2  0  2  0  2  0  2  0  2  0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  2  2  0  2  0  0  2
 0  0  0  2  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  0  0  2  0  0
 0  0  0  0  2  0  2  0  0  2  2  2  2  2  0  2  2  0  2  0  0  2  0  2  0  2  0  2  2  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  2  2  0  0  2  2  0  2  2  2  2  0  0  0  0  0  0  0  2  2  0  2  2  2  0  2  2  0  2  0  2  0  0  0  2  2  2
 0  0  0  0  0  2  0  2  2  2  2  0  2  0  2  2  0  0  2  2  2  0  0  2  0  2  2  0  2  2  0  0  0  0  2  2  2  0  0  2  0  2  2  0  2  2  0  2  0  2  0  0  2  0  2  0  0  0  2  2  2  0  0  2  0  0  2  2  0  0  2  2  2  2  0  0  0  0  0  2  2  2  2  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+71x^82+109x^84+158x^86+105x^88+56x^90+7x^92+2x^94+1x^96+1x^98+1x^160

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 0.492 seconds.