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

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+62x^86+8x^87+94x^88+184x^89+342x^90+184x^91+81x^92+8x^93+42x^94+12x^96+2x^98+2x^100+1x^104+1x^164

The gray image is a code over GF(2) with n=720, k=10 and d=344.
This code was found by Heurico 1.16 in 0.672 seconds.