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

generates a code of length 86 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+74x^81+50x^82+220x^83+63x^84+352x^85+553x^86+344x^87+53x^88+212x^89+34x^90+76x^91+9x^92+2x^94+2x^96+2x^97+1x^166

The gray image is a code over GF(2) with n=688, k=11 and d=324.
This code was found by Heurico 1.16 in 0.875 seconds.