The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+522x^85+462x^86+560x^87+480x^88+428x^89+406x^90+380x^91+244x^92+324x^93+110x^94+100x^95+10x^96+24x^97+9x^98+4x^99+22x^101+4x^102+4x^103+1x^120+1x^122

The gray image is a code over GF(2) with n=712, k=12 and d=340.
This code was found by Heurico 1.16 in 62.4 seconds.