The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+156x^83+722x^84+608x^85+804x^86+384x^87+404x^88+192x^89+250x^90+116x^91+195x^92+92x^93+90x^94+40x^95+25x^96+12x^97+3x^100+2x^104

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 0.484 seconds.