The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  0  X  1  1  1  1  1  1  X  2  1 2X  1  X  X
 0  X  0  X 2X  0 3X+2 X+2  0 2X 3X 3X  0  2 X+2  X  2  X X+2  2 3X  X 3X 3X  X X+2  0 3X 2X+2  X  2 2X+2  X  2  2 X+2
 0  0  X  X  0 X+2 3X+2 2X 2X+2 X+2 X+2 2X+2  2  X 2X+2  X X+2 X+2 3X X+2  0 2X  2 2X  0 3X 3X 2X+2 3X+2 2X+2  X 2X+2 3X+2 2X 3X  0
 0  0  0 2X+2  2 2X+2 2X 2X+2 2X+2  0 2X+2  2  0  2  0 2X 2X+2  0 2X+2  2 2X+2  0 2X+2 2X  2 2X  2 2X  0  0 2X+2 2X 2X+2  0 2X 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+334x^32+72x^33+720x^34+424x^35+1095x^36+472x^37+560x^38+56x^39+274x^40+64x^42+21x^44+2x^48+1x^56

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 4.73 seconds.