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

generates a code of length 87 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+390x^82+72x^83+577x^84+296x^85+632x^86+296x^87+680x^88+280x^89+392x^90+80x^91+239x^92+104x^94+33x^96+18x^98+4x^100+1x^104+1x^144

The gray image is a code over GF(2) with n=696, k=12 and d=328.
This code was found by Heurico 1.16 in 145 seconds.