The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+60x^30+104x^32+56x^34+256x^35+1088x^36+256x^37+112x^38+75x^40+8x^42+20x^46+11x^48+1x^56

The gray image is a code over GF(2) with n=288, k=11 and d=120.
This code was found by Heurico 1.16 in 21.4 seconds.