The generator matrix

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

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+200x^84+264x^85+603x^86+292x^87+512x^88+488x^89+501x^90+264x^91+504x^92+186x^93+171x^94+20x^95+63x^96+14x^97+2x^98+4x^101+1x^102+2x^109+2x^113+1x^122+1x^126

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 1.09 seconds.