The generator matrix

 1  0  1  1  1  2  X  1  1  1 X+2  1  1  1 X+2  1  1 X+2  1  1  2  1  1  2  1  1  2  1  1  2  0  1  1  1 X+2  1  X  1  2  1  1 X+2  1 X+2  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1
 0  1  1 X+2 X+3  1  1 X+1  X  3  1  2  X X+1  1  X X+1  1  0  1  1  0  1  1  0 X+3  1 X+2  1  1  1  2 X+3  X  1  1  1  0  1  0  X  1  X  1 X+3  3 X+3  1 X+2 X+1  3 X+3  1 X+1  3 X+1  3 X+1 X+1  1  3 X+3  3 X+3  1  0  2  2  0  X  2 X+2  X  X  0 X+2  1 X+1  1  3  0  1 X+1 X+3  1  2  2
 0  0  X  0 X+2  X  X  2  X  2  0  X X+2  2  0  0  X X+2  0 X+2  0 X+2  2 X+2  0  X  X  0  X X+2  0 X+2  2 X+2  0  2  X  0  0  X  0 X+2  X  0  2  2  X  X  2 X+2 X+2 X+2  X  0  2  0  2 X+2  X X+2 X+2  2  0  2  0  2  2  X X+2  X  0  2  0 X+2  2  X X+2  X  0 X+2  X  2  X  0 X+2  2  X
 0  0  0  2  0  2  2  2  0  2  0  2  0  0  2  2  2  0  0  2  2  2  0  0  2  0  0  0  2  2  0  0  0  2  0  2  0  2  2  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  0  2  0  0  2  2  0  0  2  0  2  0  2  2  0  0  0  0  0  2  2
 0  0  0  0  2  2  0  0  2  2  2  2  0  2  2  2  0  0  2  2  0  0  0  2  2  0  0  2  0  0  2  2  2  2  0  2  2  0  2  0  0  2  0  0  0  0  2  2  2  0  0  2  2  0  2  2  0  0  2  0  2  0  2  2  0  0  2  0  2  2  2  0  2  2  2  2  0  0  2  2  2  2  2  0  0  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+69x^82+88x^83+141x^84+72x^85+138x^86+100x^87+143x^88+40x^89+57x^90+56x^91+52x^92+16x^93+24x^94+12x^95+9x^96+5x^112+1x^132

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 0.545 seconds.