The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  2  1  1  1  X  1  1  X
 0 2X  0  0  0  0  0 2X  0  0  0 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X  0 2X 2X 2X 2X  0  0 2X 2X  0 2X 2X  0
 0  0 2X  0  0  0  0 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0  0
 0  0  0 2X  0  0  0 2X  0 2X 2X  0  0 2X  0 2X  0  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0 2X
 0  0  0  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X  0 2X 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X  0  0 2X 2X  0 2X
 0  0  0  0  0 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X  0  0  0 2X  0  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X
 0  0  0  0  0  0 2X 2X 2X  0 2X  0  0  0 2X 2X  0 2X 2X 2X  0  0 2X  0  0 2X  0  0 2X 2X 2X 2X  0  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+58x^32+64x^34+128x^35+544x^36+128x^37+64x^38+24x^40+12x^48+1x^64

The gray image is a code over GF(2) with n=288, k=10 and d=128.
This code was found by Heurico 1.16 in 0.047 seconds.