The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+78x^85+348x^86+264x^87+306x^88+248x^89+290x^90+116x^91+183x^92+94x^93+48x^94+16x^95+29x^96+12x^97+4x^98+4x^99+4x^102+1x^108+1x^110+1x^118

The gray image is a code over GF(2) with n=712, k=11 and d=340.
This code was found by Heurico 1.16 in 0.563 seconds.