The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+190x^85+774x^86+1066x^87+1096x^88+980x^89+942x^90+794x^91+649x^92+426x^93+449x^94+342x^95+156x^96+120x^97+137x^98+34x^99+8x^100+8x^101+8x^102+4x^103+1x^104+4x^105+1x^108+1x^110+1x^114

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 1.48 seconds.