The generator matrix

 1  0  0  1  1  1  2  1  1 X+2  1  1  0  2  0  X  1  1  X X+2  1  1  1  1  1  X  1  0  1  1 X+2  1  1 X+2  1  1  X  1  1  2  1  1 X+2 X+2  1  1  0  1  1  2  1  1  1 X+2  1  2  1  1  1  1  1  1  1  1  1  1  X  0  1  1  X X+2  2  X  1  1  1  1  0  1  1  X  0  2
 0  1  0  2  3  1  1  0  2  0  3  1  1  1 X+2  X  X X+1  1  1 X+2 X+3 X+2  0 X+3  1  3  1  X X+1  1  X X+3  1 X+2 X+1  1  2  1  1  0  1  1  X  X X+1  1 X+2 X+1  1  0 X+2  3  1  3  1  1  3 X+3  1 X+3 X+3 X+3  2 X+2  1  1  1  2  0  1  1  1  1  2  X  3  0  1  2  X  2  X  0
 0  0  1 X+3 X+1  2 X+1 X+2  1  1  3  X X+2  3  1  1  X X+1  3  X X+3  0  0 X+3  1  0  2  3 X+1  2  1  1 X+2 X+3  3  X X+1  3 X+2 X+3  2  3  2  1 X+2 X+3  2  2  1  X  X X+1 X+3 X+2  0  1 X+3  X  X X+1  2  3 X+3  2 X+2  1  2  X X+2 X+1 X+2  3  0 X+3  0  2  1  1 X+1 X+1  0  1  1  1

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+220x^82+136x^84+96x^86+33x^88+20x^90+2x^92+1x^96+2x^100+1x^104

The gray image is a code over GF(2) with n=336, k=9 and d=164.
This code was found by Heurico 1.16 in 53.8 seconds.