The generator matrix

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

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+104x^83+193x^84+192x^85+142x^86+88x^87+45x^88+12x^89+35x^90+28x^91+43x^92+44x^93+41x^94+28x^95+4x^96+8x^97+5x^98+8x^99+1x^102+2x^112

The gray image is a code over GF(2) with n=348, k=10 and d=166.
This code was found by Heurico 1.11 in 0.377 seconds.