The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  X  1  1  1  1  X  1  1  2  1  2  1  1 2X
 0 2X+2  0  0  0  2 2X+2  2  0 2X 2X+2 2X+2  0 2X 2X+2 2X+2  0 2X+2  2 2X  0 2X+2  0 2X 2X+2 2X 2X 2X  2  2  0  0  2  0 2X  2
 0  0 2X+2  0  2  2  2 2X  0 2X  2 2X+2  2  2 2X 2X  2  2  2 2X+2 2X+2 2X 2X  2 2X 2X 2X 2X+2 2X 2X 2X 2X+2  0 2X+2  2 2X
 0  0  0 2X+2  2 2X 2X+2 2X+2  0 2X+2 2X 2X+2  2  0 2X+2  0 2X+2  2 2X+2  0 2X 2X  2 2X 2X+2 2X 2X  2  2  0  2 2X+2 2X+2  2 2X 2X+2
 0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0 2X  0  0 2X  0 2X  0 2X  0  0 2X 2X  0 2X  0 2X  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+183x^32+64x^33+128x^34+448x^35+440x^36+448x^37+128x^38+64x^39+102x^40+39x^44+2x^48+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 1.28 seconds.