The generator matrix

 1  0  0  1  1  1  2  2 2X+2  1  1  2  1  1 3X  1  1  1  1 X+2 3X+2  1  1 X+2  1  X 3X  1  1 2X+2  1  1 3X+2  1  1  1  1 2X  1  1  1  1  1  1  1  1 2X  X  1 X+2  1 2X  1  1  1  1  1  1  X  1  1  1 X+2  1 3X 3X+2  1  1 3X+2  1  1  1 3X 2X+2 X+2 2X+2  2 2X+2  1 2X X+2  1  1  1  1  0  1  1  1
 0  1  0  0  3  3  1  X  1 2X 2X+3  1  2  1 3X+2 3X 3X+1  X 3X+3  1  1 X+1 3X+3  0 3X+2  1  1  X 2X+1  1 3X+2  1 2X+2 X+1  2 X+3  3  1 2X 2X+2 2X+1 2X+2 2X+3  1 2X X+3 3X  1 3X+2  1  1  1 3X  1 3X+2 3X+1  X  0  2 2X+2 2X 2X  X 3X+2  1  1  1 3X  1 X+2 X+3 2X+1  1  1  1  1  1  0 X+3  1  1 2X+3 2X+2  2 3X  1  0  2  X
 0  0  1 X+1 3X+1 2X 3X+3  1 3X  X 3X  3  3 2X+3  1  1 2X+1 2X  X 3X+1 3X+2 X+1  2  1 3X+3  2 2X+1  2 3X 3X+1  X 2X+1  1 2X+3  1 3X+2 3X+3 2X+1 2X+2 2X+3  0 X+3 X+2 X+3 3X+2 X+1  1  0 3X+1 2X+3 2X+2 3X+2 3X+1  3  1 3X 3X+2 3X+2  1  2 2X+3 3X+1  1 X+1  1 3X+1  2  X  0 3X+3  2 X+3 X+2 2X+1 X+2  2 3X  1 2X+3 2X+2 3X 3X+2 X+3  2  0 2X+1  2 X+2 3X
 0  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0 2X 2X  0 2X  0  0  0  0  0  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X  0 2X 2X  0  0 2X 2X 2X  0 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+168x^84+734x^85+980x^86+1238x^87+1118x^88+904x^89+770x^90+556x^91+491x^92+418x^93+263x^94+246x^95+114x^96+76x^97+42x^98+40x^99+19x^100+12x^101+1x^110+1x^112

The gray image is a code over GF(2) with n=712, k=13 and d=336.
This code was found by Heurico 1.16 in 1.33 seconds.