The generator matrix

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

generates a code of length 86 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+408x^83+267x^84+320x^85+112x^86+300x^87+253x^88+352x^89+16x^91+5x^92+12x^95+2x^128

The gray image is a code over GF(2) with n=688, k=11 and d=332.
This code was found by Heurico 1.16 in 0.781 seconds.