The generator matrix

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

generates a code of length 36 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+146x^30+1048x^31+2527x^32+4438x^33+7894x^34+10140x^35+13070x^36+10118x^37+8290x^38+4554x^39+2052x^40+834x^41+290x^42+90x^43+30x^44+2x^45+4x^46+6x^47+2x^51

The gray image is a code over GF(2) with n=288, k=16 and d=120.
This code was found by Heurico 1.16 in 17.2 seconds.