The generator matrix

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

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+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.