The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2) 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 0.89 seconds.