The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+70x^32+144x^33+291x^34+260x^35+591x^36+244x^37+244x^38+84x^39+57x^40+28x^41+24x^42+8x^43+1x^50+1x^60

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 0.063 seconds.