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

generates a code of length 90 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+28x^89+82x^90+6x^92+4x^94+4x^97+2x^106+1x^120

The gray image is a code over GF(2) with n=720, k=7 and d=356.
This code was found by Heurico 1.16 in 0.515 seconds.