The generator matrix

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

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+407x^84+72x^85+572x^86+272x^87+598x^88+336x^89+688x^90+272x^91+421x^92+72x^93+244x^94+60x^96+56x^98+15x^100+8x^102+1x^104+1x^148

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 3.62 seconds.