The generator matrix

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

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+145x^32+272x^33+710x^34+572x^35+749x^36+548x^37+690x^38+260x^39+106x^40+12x^41+14x^42+13x^44+2x^46+2x^48

The gray image is a code over GF(2) with n=288, k=12 and d=128.
This code was found by Heurico 1.16 in 0.125 seconds.