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  0  X 2X+2  X  0  X 2X+2  X  0  X 2X+2  X  X  X  0  X 2X+2  X  X  X  X  1  1  1  1  1  1  X  X  X  X  1  1 2X  2 2X  2  X  X  X  X 2X  2 2X  2  1  1  1  1  X  1  1  1  1  X 2X  1
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 X+2 2X+2 3X  0 X+2 2X+2  X 2X 3X+2  2  X 2X 3X+2  2 3X 2X 3X+2  2  X 2X 3X+2  2 3X X+2  X 3X  X X+2  X 3X  X X+2  X 3X  X  0 2X+2 X+2  X 3X  X  0 2X+2  0 2X+2  0 2X 2X+2 2X+2 2X+2 2X+2 3X+2  X 3X+2  X  0 2X  X  X  X  X 3X+2  X 3X+2  X  X  X  X  X  0 2X  0 2X  2  2  2  2  2 2X 2X  0
 0  0 2X  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X  0  0 2X 2X  0  0  0  0  0
 0  0  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0  0  0  0

generates a code of length 90 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+18x^88+276x^89+18x^90+128x^91+12x^92+40x^93+12x^94+1x^96+4x^97+1x^98+1x^130

The gray image is a code over GF(2) with n=720, k=9 and d=352.
This code was found by Heurico 1.16 in 0.828 seconds.