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

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

Homogenous weight enumerator: w(x)=1x^0+70x^89+140x^90+16x^91+12x^92+4x^94+3x^96+8x^97+2x^105

The gray image is a code over GF(2) with n=720, k=8 and d=356.
This code was found by Heurico 1.16 in 2 seconds.