The generator matrix

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