The generator matrix

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

generates a code of length 90 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+136x^86+822x^87+574x^88+682x^89+376x^90+526x^91+214x^92+214x^93+120x^94+156x^95+56x^96+120x^97+37x^98+40x^99+18x^100+1x^102+1x^104+1x^106+1x^110

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.