The generator matrix

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

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+327x^32+32x^33+704x^34+480x^35+1113x^36+480x^37+600x^38+32x^39+235x^40+72x^42+18x^44+1x^48+1x^60

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 16 seconds.