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

generates a code of length 87 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+320x^83+66x^84+120x^85+192x^86+672x^87+214x^88+112x^89+288x^91+36x^92+24x^93+2x^108+1x^128

The gray image is a code over GF(2) with n=696, k=11 and d=332.
This code was found by Heurico 1.16 in 0.531 seconds.