The generator matrix

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

generates a code of length 36 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+50x^31+708x^32+1108x^33+2294x^34+2416x^35+3483x^36+2396x^37+2088x^38+902x^39+696x^40+144x^41+56x^42+24x^43+15x^44+1x^48+2x^50

The gray image is a code over GF(2) with n=288, k=14 and d=124.
This code was found by Heurico 1.16 in 1.25 seconds.