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

generates a code of length 90 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+182x^86+127x^88+1428x^90+127x^92+182x^94+1x^180

The gray image is a code over GF(2) with n=720, k=11 and d=344.
This code was found by Heurico 1.16 in 9.44 seconds.