The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X  1  1 3X+2  1  2  1  1  1  1  1  0 3X  1  1  1  1  2 3X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1 X+2  1 2X+2  X 2X  1  1  X 2X X+2 X+2 2X+2 2X+2  X
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+1  1  2 X+3  1 2X+3  1 3X+2 3X  0 X+1 2X+1  1  1  2 3X X+3 2X+3  1  1 2X X+2 2X+2  X 2X X+2 2X+2  X 2X X+2 2X+2  X 2X X+2 2X+2  X 3X+1  3 3X+3  1 3X+1  3 3X+3  1  1 3X+1  1  3  1  1  1 3X+3  1  1  1  1  1  1  0 3X+2
 0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X  0 2X  0 2X  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0  0  0  0 2X 2X  0 2X 2X  0  0  0 2X
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X 2X  0  0  0  0 2X  0 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+136x^86+288x^87+186x^88+288x^89+104x^90+18x^92+1x^108+1x^116+1x^120

The gray image is a code over GF(2) with n=704, k=10 and d=344.
This code was found by Heurico 1.16 in 0.828 seconds.