The generator matrix

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

generates a code of length 88 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+102x^86+244x^87+388x^88+184x^89+58x^90+20x^91+24x^92+2x^108+1x^128

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 0.609 seconds.