The generator matrix

 1  0  1  1  1 3X+2  1  1 2X+2  1  1  X  1  1 2X  1 X+2  1  1  2  1  1  1  0  1 3X  1  1 2X+2  1  1 X+2  1  1 3X  1  1  1 X+2  1 2X  1  1 3X  1  1  2  1  X  1  X  1  0 2X  1  1  1  1 2X+2 2X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 3X+2  1  1  0  1  1  X  1
 0  1 X+1 3X+2  3  1 2X X+3  1 2X+2 2X+1  1  X X+1  1 2X+3  1 X+2  1  1  2 3X  3  1 3X+3  1 2X 2X+1  1 3X+2 X+1  1  X 3X+3  1  2 3X+2 3X+1  1 2X+3  1  X 3X+3  1 2X+2  1  1  0  0  0 3X 2X+3  X  1  0 2X+1 2X+3  2  1  1  2 2X X+2 X+2  2 X+2  X 3X X+2 2X  2  X 3X 3X+2 X+2 3X+1 2X+1 2X+1  3 3X+3 3X+1 3X+1  1 2X+1 3X  1 X+2 3X+1 X+2 2X
 0  0  2  2 2X  2 2X+2 2X+2 2X 2X  0 2X+2 2X+2  0 2X+2  2 2X  0 2X+2  2  2 2X  0 2X 2X  0 2X+2 2X  0 2X+2 2X  0  2  0 2X  2 2X 2X+2 2X+2 2X+2  2  0  2  2  0  2 2X+2 2X  0  2 2X 2X 2X 2X  2 2X  0 2X+2 2X  0 2X+2 2X 2X 2X 2X 2X+2 2X+2  2  2  0  0  0  0  2  2  2  2  0  2  0  2  0  2 2X+2 2X 2X+2  0 2X+2 2X+2  2
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X  0 2X 2X  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0 2X  0  0  0 2X 2X 2X  0 2X  0 2X  0  0 2X  0 2X 2X 2X  0  0 2X  0  0 2X 2X 2X  0  0  0 2X  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+57x^86+346x^87+288x^88+282x^89+262x^90+244x^91+191x^92+184x^93+63x^94+88x^95+31x^96+6x^97+1x^98+2x^111+1x^116+1x^130

The gray image is a code over GF(2) with n=720, k=11 and d=344.
This code was found by Heurico 1.16 in 0.906 seconds.