The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+118x^81+384x^82+458x^83+542x^84+390x^85+549x^86+326x^87+382x^88+362x^89+362x^90+104x^91+68x^92+24x^93+6x^94+6x^95+6x^96+2x^101+2x^106+2x^107+1x^118+1x^120

The gray image is a code over GF(2) with n=688, k=12 and d=324.
This code was found by Heurico 1.16 in 0.812 seconds.