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

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

Homogenous weight enumerator: w(x)=1x^0+162x^32+192x^33+176x^34+320x^35+376x^36+192x^37+416x^38+64x^39+116x^40+16x^42+16x^44+1x^64

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.