The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+438x^83+278x^84+292x^85+211x^86+264x^87+148x^88+260x^89+52x^90+58x^91+12x^92+20x^93+4x^95+4x^97+4x^99+1x^118+1x^120

The gray image is a code over GF(2) with n=688, k=11 and d=332.
This code was found by Heurico 1.16 in 41.2 seconds.