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

generates a code of length 88 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+48x^86+32x^87+368x^88+32x^89+12x^90+12x^92+4x^94+1x^112+2x^120

The gray image is a code over GF(2) with n=704, k=9 and d=344.
This code was found by Heurico 1.16 in 0.765 seconds.