The generator matrix

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

generates a code of length 90 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+232x^85+707x^86+922x^87+1397x^88+932x^89+928x^90+744x^91+587x^92+488x^93+336x^94+302x^95+288x^96+132x^97+140x^98+24x^99+29x^100+1x^104+1x^110+1x^112

The gray image is a code over GF(2) with n=720, k=13 and d=340.
This code was found by Heurico 1.16 in 1.34 seconds.