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  X  0  X X^2+2  X  0  X X^2+2  X  0  X X^2+2  X  0  X  2  X X^2+2  X X^2  X  X  0  X  X  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X+2 X^2+2  0 X^2+X X^2+2  X  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2  X  0 X^2+X X^2+2  X  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X X^2+X  X X+2  X X^2+X  X X+2  X X^2+X  X X+2  X X^2+X  X X^2+X+2  X X+2  X  X  X X+2  0  X  0  0  0
 0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  0  0  2  2  2  0  0  2  0  0  2  2  2  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  0  0  2  2  0  0  0  0  2  2  0  0  2  2  0  0  0  2  0  2  2  2  0  0  2  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  2  0  0  2  2  2  0  0  0  2  2  0  0  0  2  2  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  0  2  2  2  0  0  0  0
 0  0  0  0  2  2  2  2  2  0  2  0  0  2  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  0  0  0  0  2  2  0  0  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  0  0  2  2  0  2  0  0  2  2  0  0  2  2  0  0  2  0  2  0  2  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+49x^86+100x^87+110x^88+128x^89+235x^90+152x^91+79x^92+128x^93+34x^94+4x^95+1x^96+1x^108+1x^110+1x^130

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 0.875 seconds.