The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+141x^82+227x^84+169x^86+173x^88+166x^90+97x^92+27x^94+12x^96+8x^98+2x^120+1x^122

The gray image is a code over GF(2) with n=348, k=10 and d=164.
This code was found by Heurico 1.16 in 0.433 seconds.