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

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+152x^87+102x^88+294x^89+60x^90+172x^91+78x^92+88x^93+2x^94+60x^95+10x^96+2x^97+1x^104+1x^106+1x^130

The gray image is a code over GF(2) with n=720, k=10 and d=348.
This code was found by Heurico 1.16 in 1.16 seconds.