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+X  1 X^2+2  1  1  1 X+2  1  2  1  1 X^2  1  1 X^2+X  1  1  1 X+2  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^2+2 X^2+X+2  X  0 X^2+2  2  X  X  0
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3 X^2+2  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 X^2+1  1 X^2+2  1 X^2+X+3 X+2  3  1  2  1 X+1 X^2+X  1 X^2+X+3 X^2+1  1 X^2 X+2  3  1 X^2+X+2  0  X X^2+2  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X X+3 X^2+3 X^2+X+1  1 X+1 X^2+1 X+1 X^2+1 X^2+X+3  3 X+3 X^2+3 X^2+X+3 X^2+X+1  3  1  1  1  1  1  1  1 X^2  1  1  1
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  0  2  0  2  2  2  2  0  0  2  0  0  2  2  0  0  0  2  2  0  2  2  2  0  0  0  0  2  2  0  0  2  2  0  2  0  2  2  0  2  0  2  0  2  2  2  0
 0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  2  2  0  0  0  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  0  2  0  2  0  0  2  2  0  0  2  0  2  0  0  0  0  2  2  2  2  0  2  2  2  2  0  0  0  2  0  0  2  2  2  2  2  2  0
 0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  0  2  2  0  2  0  2  0  0  2  0  2  0  2  0  0  2  0  2  2  0  0  0  2  2  0  0  0  0  2  2  2  0  2  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+314x^86+60x^87+144x^88+208x^89+662x^90+200x^91+80x^92+16x^93+302x^94+28x^95+30x^96+2x^114+1x^128

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 0.594 seconds.