The generator matrix

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

generates a code of length 86 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+16x^85+208x^86+16x^87+2x^88+8x^90+2x^92+1x^96+2x^100

The gray image is a code over GF(2) with n=688, k=8 and d=340.
This code was found by Heurico 1.16 in 0.266 seconds.