The generator matrix

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

generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+161x^84+354x^85+491x^86+478x^87+473x^88+342x^89+438x^90+386x^91+433x^92+310x^93+151x^94+26x^95+15x^96+18x^97+5x^98+6x^99+2x^108+2x^110+2x^112+1x^122+1x^128

The gray image is a code over GF(2) with n=712, k=12 and d=336.
This code was found by Heurico 1.16 in 0.891 seconds.