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

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

Homogenous weight enumerator: w(x)=1x^0+202x^86+305x^88+1042x^90+298x^92+190x^94+2x^96+6x^98+1x^100+1x^172

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 2.02 seconds.