The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  2  1  1  1  1 X^2+X  1  1  X X^2+X+2  1 X+2  1  1 X^2+2 X^2  1  1  2 X^2  1  1  1  1  1  1  X  1  1  2  1  1  1 X^2+X+2  1  0  1  1  2 X^2 X^2 X^2+2 X^2+2  X  2 X^2  0 X^2+X X+2 X+2 X^2+X+2 X+2 X+2  X X+2  0  1  1  1  1  1  1  1  1  1 X^2  1 X^2+X+2  1  1  1  1  1  1  X X^2 X^2+X+2 X^2  1  1
 0  1  1 X^2 X+1  1  X X^2+X+1  1  X  1 X^2+X+1 X+1 X^2+1  2  1  1 X^2+2  1  1 X+2  1 X+2 X^2+3  1  1 X+3 X^2  1  1  2 X^2+3 X^2+X+2 X^2+X+1 X^2+X+3  2  1 X^2+X+2 X^2+3  1 X^2+X+2  3 X^2  1  1  1 X^2+X+2 X+1  1  1  1  1  1 X^2  1  1  1  1  1  1  1  1  1  1  1  X  0  2  0  0  0  2 X+2 X+2 X^2+X+2  1  X  1 X^2+X X^2+2  0  X X^2 X^2 X^2+X+2  X  1  1  3 X^2+3
 0  0  X X+2  2 X+2 X+2  X X^2+2 X^2 X+2 X^2+2 X^2+X X^2+X X^2  2 X^2+2 X^2+X X^2+X X+2  0 X^2 X^2+X  2  0  X X^2+2 X^2 X^2+2 X^2+X+2 X+2  X  2 X^2+X+2  0 X^2+X+2  2 X^2 X^2+2 X^2 X^2+X+2 X^2+X+2  2 X^2+X  0 X^2+X X+2  X  0 X^2  2 X^2+2  X  X X^2+X X+2 X^2+X+2 X^2+2  2  X X^2 X^2+X+2 X+2  0 X^2+X  2 X^2  0 X^2+2 X^2+X+2 X^2+X  2 X+2  X  0 X^2+X X^2+X+2  X X^2 X+2  X X^2+2  0 X^2+X X^2+X+2 X+2  0  0 X+2 X^2+X

generates a code of length 90 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+390x^87+272x^88+400x^89+152x^90+304x^91+166x^92+216x^93+24x^94+62x^95+22x^96+20x^97+8x^99+1x^100+4x^101+4x^103+1x^108+1x^136

The gray image is a code over GF(2) with n=720, k=11 and d=348.
This code was found by Heurico 1.16 in 1.14 seconds.