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

generates a code of length 90 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+234x^86+674x^87+680x^88+644x^89+412x^90+392x^91+232x^92+216x^93+222x^94+118x^95+57x^96+112x^97+42x^98+16x^99+37x^100+4x^101+1x^102+1x^108+1x^110

The gray image is a code over GF(2) with n=720, k=12 and d=344.
This code was found by Heurico 1.16 in 0.515 seconds.