The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+130x^83+130x^84+194x^85+119x^86+138x^87+54x^88+60x^89+20x^90+18x^91+24x^92+58x^93+20x^94+34x^95+4x^96+4x^97+9x^100+4x^101+1x^104+1x^108+1x^118

The gray image is a code over GF(2) with n=348, k=10 and d=166.
This code was found by Heurico 1.16 in 0.414 seconds.