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

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+204x^85+42x^86+218x^87+220x^88+700x^89+209x^90+212x^91+30x^92+196x^93+4x^94+2x^95+4x^96+4x^97+1x^98+1x^168

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 40.9 seconds.