The generator matrix

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

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+96x^32+120x^33+274x^34+328x^35+440x^36+328x^37+246x^38+120x^39+73x^40+10x^42+5x^44+6x^46+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 0.078 seconds.