The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+46x^84+92x^85+116x^86+96x^87+50x^88+48x^89+17x^90+16x^91+10x^92+4x^93+9x^96+4x^100+1x^102+1x^106+1x^110

The gray image is a code over GF(2) with n=348, k=9 and d=168.
This code was found by Heurico 1.13 in 0.203 seconds.