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

generates a code of length 90 over Z4[X]/(X^3+2,2X) 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 0.844 seconds.