The generator matrix

 1  0  0  1  1  1  2  1  1  2  1  1  0  0  1  1  1  1  X  1  1  0 X+2  1  2  0  1  X  X  X X^2+X+2  1  1 X^2+2  1 X^2+2  1 X+2  1  1 X+2  1 X^2+X+2 X^2+X  1  1  1 X^2  1  1 X^2  1 X+2  1  1  X  1  1  1  1  1  1 X^2+2  1  1  1 X^2+X+2  1 X^2 X^2+X X^2+X+2 X^2+2  1  1  1  1  1  1 X^2  1  1  X  2  1  1 X^2+X  X  1 X^2  1
 0  1  0  2 X^2+1 X^2+3  1  0 X^2+1  1  2 X^2+3  1 X^2+X X+2  X X^2+X+3 X^2+X+1 X^2+X+2 X^2+X+3 X^2+X+1  1  1  X  1  X X+2  1  1 X^2  1 X^2+X X+3  1  0  1 X^2+X  X X+3  2  1  0 X^2+2  1 X+1 X^2+X  1 X^2  2  3  X X^2  1 X^2+1  X  1  1 X+2 X+3 X^2+X+3 X+3 X^2+X+1  1 X^2+X  3 X^2+X+2 X+2  3  1  1  1  1 X+3 X^2+3  3 X^2+2 X^2+2 X^2+X+2  1 X^2+X+1  0  1 X^2 X^2+3 X^2+X+2  1  0 X^2  1  2
 0  0  1 X+3 X+1  2 X^2+X+1 X^2+X X^2+1  3 X^2+3 X^2+X+2 X^2+X+2  1 X^2+X X^2+3 X+1  2  1 X^2+1 X^2+X+2 X+2  1 X+3 X^2+3  1  0 X^2+2 X+2  1 X+1 X+2  1 X+1 X^2+X+1 X^2  2  1  0  1 X^2+3 X+2  1 X^2+X+2 X^2+X+3 X^2+X+1  3  1 X^2  2  1 X^2 X+1 X+2  3  0 X^2+X+3 X^2 X+3 X+2 X^2+3 X^2+2  0 X^2+2 X^2+X+2 X^2+X+2  1 X^2+1  3 X^2+1  2 X^2+X X+2 X^2  X X^2+X X^2+X+1  1 X+2 X+2  X X^2+X+2  1 X^2+2 X+1 X^2+X+3  1  1  2 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+200x^86+658x^87+718x^88+640x^89+528x^90+314x^91+247x^92+188x^93+176x^94+144x^95+56x^96+104x^97+68x^98+32x^99+16x^100+1x^102+2x^104+3x^106

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 0.516 seconds.