The generator matrix

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

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+52x^82+32x^83+101x^84+32x^85+18x^86+4x^88+8x^90+3x^92+2x^94+2x^96+1x^104

The gray image is a code over GF(2) with n=336, k=8 and d=164.
This code was found by Heurico 1.16 in 0.311 seconds.