The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+341x^30+1754x^31+4392x^32+9468x^33+15162x^34+21236x^35+25611x^36+22204x^37+15680x^38+9220x^39+3791x^40+1532x^41+520x^42+108x^43+29x^44+12x^45+7x^46+2x^47+2x^50

The gray image is a code over GF(2) with n=288, k=17 and d=120.
This code was found by Heurico 1.16 in 73.9 seconds.