The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+438x^84+194x^85+415x^86+116x^87+352x^88+152x^89+238x^90+44x^91+68x^92+6x^93+14x^94+4x^100+4x^102+1x^120+1x^126

The gray image is a code over GF(2) with n=696, k=11 and d=336.
This code was found by Heurico 1.16 in 191 seconds.