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

generates a code of length 87 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+134x^85+200x^86+406x^87+166x^88+66x^89+14x^90+34x^91+1x^104+1x^106+1x^130

The gray image is a code over GF(2) with n=696, k=10 and d=340.
This code was found by Heurico 1.16 in 0.562 seconds.