The generator matrix

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

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+414x^83+489x^84+702x^85+413x^86+462x^87+274x^88+538x^89+314x^90+260x^91+59x^92+72x^93+35x^94+20x^95+4x^96+8x^97+4x^98+8x^99+4x^100+8x^101+1x^102+4x^103+1x^118+1x^120

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 30.9 seconds.