The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+208x^83+724x^84+576x^85+760x^86+328x^87+400x^88+184x^89+364x^90+160x^91+137x^92+96x^93+89x^94+40x^95+16x^96+8x^97+2x^98+1x^102+1x^104+1x^108

The gray image is a code over GF(2) with n=696, k=12 and d=332.
This code was found by Heurico 1.16 in 0.516 seconds.