The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+391x^86+250x^87+434x^88+82x^89+327x^90+180x^91+276x^92+40x^93+25x^94+14x^95+8x^96+6x^97+4x^98+4x^99+4x^102+1x^128+1x^130

The gray image is a code over GF(2) with n=712, k=11 and d=344.
This code was found by Heurico 1.16 in 24.7 seconds.