The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+305x^30+1858x^31+4482x^32+9372x^33+14579x^34+22292x^35+23957x^36+24190x^37+14963x^38+9022x^39+3829x^40+1464x^41+567x^42+136x^43+35x^44+14x^45+4x^47+2x^50

The gray image is a code over GF(2) with n=288, k=17 and d=120.
This code was found by Heurico 1.16 in 73.7 seconds.