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  0  X  0  X  X  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  2  X  0  X  0  X  X  0  X  X  X  X  X  2  X
 0  X  0  X  0  0 X+2 X+2  0  0  X X+2  0  0 X+2  X  0  0  X  X  0  0 X+2 X+2  0  0  X X+2  0 X+2  0  X  2  2  2  2  2  2  2  X  2  X  2 X+2  2 X+2  2  X  2 X+2 X+2  2  2  X X+2  2  X  2  X X+2  2  2  2 X+2  2  X  2  X  2 X+2  X  X X+2  X X+2  X X+2 X+2  X  0  2  0  2  2  X  2
 0  0  X  X  0 X+2 X+2  0  0 X+2  X  0  0  X X+2  0  2 X+2 X+2  2  2  X  X  2  2 X+2 X+2  2  2  X  X  2  X  X  X  X  2  2  2  X  X  2  2 X+2  X  0  2  X X+2  0 X+2 X+2  2  2  2  0 X+2  X  0  X  0  X X+2  X  0  0  0 X+2 X+2  2  X X+2 X+2 X+2  0  0  0 X+2  0  0  2  2  0 X+2  2  X
 0  0  0  2  0  0  2  0  2  2  0  2  2  2  0  2  2  0  2  0  2  0  2  0  0  2  0  2  0  0  2  2  0  2  2  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  0  2  2  0  0  0  0  0  2  2  0  0  0  2  0  2  2  0  2  2  2  0  0
 0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  0  0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  2  0  2  0  2  2  0  2  0  2  2  0  2  0  2  2  0  0  0  2  0  2  0  0  2  0  2  0  2  2  2  0  2  2  0  2  0  0  0  2  0  2  2  0  2  2  0  0  0  0  0  2  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+46x^82+68x^83+62x^84+84x^85+52x^86+40x^87+50x^88+40x^89+22x^90+20x^91+12x^92+4x^93+8x^94+2x^100+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 0.477 seconds.