The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1  1 2X  1  1
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 X+2 2X+2 3X  0 X+2 2X+2 3X 2X 3X+2  2 3X  0 X+2 2X+2 3X 2X+2 X+2  2 3X+2  0 2X 2X 3X  X 2X  0  0
 0  0 2X  0  0  0  0 2X  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0  0  0  0 2X  0 2X  0 2X  0  0 2X  0  0  0
 0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0  0
 0  0  0  0 2X 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X 2X  0  0  0 2X 2X 2X  0 2X 2X 2X  0  0  0  0  0  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+43x^32+496x^34+51x^36+352x^38+20x^40+48x^42+12x^44+1x^68

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 0.031 seconds.