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

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

Homogenous weight enumerator: w(x)=1x^0+34x^90+12x^91+1x^92+6x^93+1x^94+4x^95+2x^96+2x^97+1x^98

The gray image is a code over GF(2) with n=720, k=6 and d=360.
This code was found by Heurico 1.16 in 0.515 seconds.