The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+173x^32+732x^33+1191x^34+1484x^35+1471x^36+1268x^37+776x^38+660x^39+306x^40+64x^41+39x^42+16x^43+8x^44+2x^46+1x^52

The gray image is a code over GF(2) with n=288, k=13 and d=128.
This code was found by Heurico 1.16 in 0.344 seconds.