The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  0  X  0  X  0  X  X  X  X  X  X  2  X  X  2  X  2  X  2  1  1  1  1  1  1  2  1  1  X  0  X  X  0  X  0  X  2  X  0  X  2  X  2  X  2  X  X  1  1  X  X  X
 0  X  0 X+2  0 X+2  0  X  0 X+2  0  X  0 X+2  0  X  2 X+2  2  X  2 X+2  2  X  2 X+2  2  X  2 X+2  2  X X+2  X X+2  X X+2  X X+2  X  0  0  0  2  2  X  X  2  X  X  X  X  X  X  0  0  2  2  0  0  2  0  0 X+2  X X+2  2  X X+2  X  X  X X+2  X  X  X  X  X  X  X  0  2  2  2  0  0  0
 0  0  2  0  0  0  2  0  0  2  0  2  2  2  2  2  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  2  0  0  0  0  2  2  2  2  0  2  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  0  2  0  0  2  2  2  0  0  2  2  2  2  0  0  2  2  0  0  2  0  2  2  0  2  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  2  2  0  0  2  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  0  2  2  0  2  0  0  2  2  0  2  0  2  0  2  0  0  2  0  2  0  0  2  2  2  2  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  2  0  0  0  2  2  0  2  0  0  2  0  2  2  0  0  2  2  0  2  0  2  2  0  2  0  2  0  2  2  0  0  2  0  2  2  0  2  2  0  0  0  2  2  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  0  2  2  0  0  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+31x^84+88x^86+116x^88+4x^90+8x^92+3x^96+4x^98+1x^116

The gray image is a code over GF(2) with n=348, k=8 and d=168.
This code was found by Heurico 1.16 in 0.476 seconds.