The generator matrix

 1  0  1  1  1  2  1  1  X  1  1  X  1  1  0  1  1  0  1  1  X  1  1  X  1  1  X  1  2  1  1  0  1 X+2  1  1  2  1  1 X+2  1  1  1  2  1  1  1  X  X  X  1  X  1  1  1  1  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X+2  1 X+2  1  1 X+2 X+2  1  X  1
 0  1  1  0 X+1  1 X+3  0  1  2  1  1  0 X+1  1  2 X+1  1  0  1  1  0  1  1 X+2 X+3  1 X+2  1  1 X+1  1  3  1  X X+2  1 X+3  3  1  X X+2 X+3  1 X+2  X  1  1  2  0  0  2  X  0  X X+2  2  1  3  X X+2 X+2  2  2  0  2  X  0  X X+2  0 X+2  2  1  3 X+2  1  1  2  1 X+3  3  1  1 X+2  1  0
 0  0  X  0  0  0  0  X  X  X  X  X  2  2  2  2  2  2 X+2 X+2 X+2 X+2 X+2 X+2  X  X  0  0 X+2  2  X  X  0  0  0 X+2 X+2 X+2  2  2  X  2 X+2  X  2 X+2  0  2 X+2  X  2  2  0  2  X  X  2 X+2  0  0 X+2 X+2  2 X+2  X  X  2 X+2  2  0 X+2  0  X X+2  X  2  X  2  0  X  0  X  0 X+2  X  2  0
 0  0  0  X  2 X+2 X+2  X  2  2 X+2  X  2  0  2 X+2  X  X  0  X X+2 X+2  2  0  X  0  X  0  2  X X+2  X  0  2 X+2  0  X X+2  0  2  0 X+2  0  2  0  X  X  X  2 X+2 X+2 X+2  0  X  2  0  0  2 X+2  X X+2  X  2  0  2  0 X+2  2  X  2  X X+2 X+2  0  2  2  0 X+2  2 X+2  X  X  0  0  X  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+40x^82+142x^83+137x^84+78x^85+106x^86+136x^87+97x^88+52x^89+53x^90+50x^91+47x^92+24x^93+17x^94+20x^95+6x^96+4x^97+6x^98+4x^99+2x^101+1x^122+1x^126

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 0.425 seconds.