The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+12x^86+216x^87+14x^88+8x^91+2x^94+1x^96+2x^102

The gray image is a code over GF(2) with n=696, k=8 and d=344.
This code was found by Heurico 1.16 in 0.266 seconds.