The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 2X  1  1  1  X  1  1  1  1  1  1 2X+2  1  0  1  1  0  0 2X
 0  X  0 3X+2 2X+2 X+2  2  X  0 3X+2  2 3X 2X X+2  0 3X+2 3X+2  X 2X X+2  X  2 2X+2  0  2 2X 3X 3X  X  X  0 2X  2  X 2X  X
 0  0  2  0 2X+2 2X+2 2X 2X+2  0 2X  0  0 2X+2 2X+2  2 2X  2 2X+2  2 2X+2 2X+2 2X+2 2X+2 2X  2  0  2  2 2X+2  2 2X+2 2X+2 2X 2X 2X+2 2X
 0  0  0 2X  0  0 2X  0  0 2X 2X  0 2X 2X 2X  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0  0 2X
 0  0  0  0 2X  0  0 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X 2X 2X  0  0  0  0 2X  0  0 2X 2X  0 2X  0 2X 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+94x^32+192x^33+198x^34+396x^35+380x^36+392x^37+116x^38+144x^39+63x^40+24x^41+22x^42+4x^43+20x^44+1x^48+1x^56

The gray image is a code over GF(2) with n=288, k=11 and d=128.
This code was found by Heurico 1.16 in 0.078 seconds.