The generator matrix

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

generates a code of length 86 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+58x^84+162x^85+90x^86+128x^87+37x^88+28x^89+4x^90+2x^93+1x^98+1x^122

The gray image is a code over GF(2) with n=688, k=9 and d=336.
This code was found by Heurico 1.16 in 0.437 seconds.