The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X+2  1  1 X^2+X  1 X^2+2  1  1  1  1  1  0 X+2  1  1  1  1 X^2+2 X^2+X  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  2 X^2+X+2 X^2  X  2 X^2+X+2  2 X^2+X+2 X^2  2
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X  3  1 X^2+2 X^2+X+3  1 X^2+1  1 X^2+X X+2  0 X+1  3  1  1 X^2+2 X+2 X^2+X+3 X^2+1  1  1  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2  X X+3 X^2+3 X^2+X+1  1 X+3 X^2+3 X^2+X+1  1 X+3 X^2+3 X^2+X+1  1 X+3 X^2+3 X^2+X+1  1  1  1  1  1  1  1  1  1  0  0
 0  0  2  0  2  0  2  0  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  0  2  0  2  0  0  0  2  2  0  2  0  2  2  0  2  0  0  2  2  0  0  2  2  2  0  0  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  0  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  0  2  2  0  0  0  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  2  2  0  0  0  2  0  0  0  2  2  2  2  2  0  0  0  2  0  2  0  2  0  0  2  0  2  2  0  0  2  2  0  2  0  0  2  2  0  0  2  0  2  2  0  0  2  2  0  2  0  0  2  2  0  0  2  0  2  2  0  0  2  2  0  2  0  0  2  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+300x^88+304x^90+256x^91+144x^92+16x^94+2x^112+1x^128

The gray image is a code over GF(2) with n=720, k=10 and d=352.
This code was found by Heurico 1.16 in 0.547 seconds.