The generator matrix

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

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+171x^82+392x^83+408x^84+488x^85+410x^86+564x^87+293x^88+528x^89+296x^90+256x^91+139x^92+72x^93+40x^94+4x^95+20x^96+5x^98+1x^100+4x^102+2x^110+2x^120

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 1.05 seconds.