The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X+2  1  1  1  1 X^2  2  1  1  1  1  2  1  1  X  1  1 X^2+X  1  X  1  1  1  1 X^2+X  1  1  1 X^2+X X+2  1  1 X^2  1  1  1  1  1 X^2 X^2  1  1  1  1  1  1  1  1  1  1  1  1 X+2 X+2  1 X^2+X X^2+2  1  1  1 X^2  1  2  2  1  1  1  1  2  1  1  1  X  2 X^2+X+2  1 X^2  X
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+1 X^2+X+2  1  1  0 X^2+3  2  3  1  1  X X+1 X^2+X X+3  1 X^2 X^2+1  1 X^2+X+3 X^2+2  1 X^2+1  1  2 X^2+X+2 X+1  X  1 X^2+X+1 X^2+1 X^2+X+2  1  1 X^2+X+1 X^2  1  3 X^2+X+3 X^2+X+2  1 X+2  1  X  0 X^2+2 X^2+1  3 X+1 X+1 X^2+X X+3 X^2+X+3  X  X X+1  1  1 X^2  1  1  2 X+2 X^2+2  1 X^2+1  0  1  0 X^2+3  X X+2  1 X^2+1 X^2+X  3 X+2  1  1  1  1 X^2+2
 0  0  X  0 X+2  X X+2  2  0  2 X+2 X^2+X+2 X^2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X^2+X X+2 X^2 X^2+X X^2+X X^2 X^2 X^2 X^2+X  X X^2+2 X^2+X X^2+2  X  X X+2 X+2 X^2+X+2  2 X^2+X+2  X  0 X^2+X+2 X^2+X  2 X^2+2 X^2  2  0  2 X^2 X^2  0 X^2 X^2+X+2  2  2 X^2 X^2+X+2  X  2  0  0 X^2+X+2 X+2 X^2+X+2 X^2+2 X^2 X^2+X X^2+X+2  2 X^2+X+2 X^2 X^2  X  0 X^2+2  X X+2  2 X+2  X X^2+2 X^2+X+2  0 X+2 X^2 X+2 X^2+X X+2 X^2+2 X^2+2 X^2+X+2
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  2  2  0  0  0  2  2  0  2  0  2  2  2  0  2  0  2  0  0  2  2  2  0  0  0  0  0  2  2  0  0  2  2  0  2  0  2  0  2  0  0  0  2  0  2  0  0  2  0  2  2  0  2  2  0  2  0  2  0  2  2  0  0  0  2  0  0  0  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+683x^86+152x^87+856x^88+120x^89+730x^90+128x^91+680x^92+64x^93+456x^94+40x^95+123x^96+8x^97+22x^98+29x^102+1x^104+2x^112+1x^120

The gray image is a code over GF(2) with n=720, k=12 and d=344.
This code was found by Heurico 1.16 in 3.64 seconds.