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

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

Homogenous weight enumerator: w(x)=1x^0+128x^86+105x^88+12x^90+3x^92+4x^94+2x^96+1x^100

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 0.735 seconds.