The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+54x^33+200x^34+150x^35+282x^36+114x^37+108x^38+66x^39+44x^40+2x^42+2x^46+1x^48

The gray image is a code over GF(2) with n=288, k=10 and d=132.
This code was found by Heurico 1.16 in 0.031 seconds.