The generator matrix

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

generates a code of length 90 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+382x^87+277x^88+294x^89+230x^90+274x^91+240x^92+286x^93+16x^94+20x^95+2x^96+4x^97+20x^99+1x^130+1x^138

The gray image is a code over GF(2) with n=720, k=11 and d=348.
This code was found by Heurico 1.16 in 54.4 seconds.