The generator matrix

 1  0  0  1  1  1  X  1  1 X^2+X+2  1  1 X+2 X^2+X+2  1  1  0  1 X^2+2  2  1 X+2  2  1  1 X^2  1  1 X+2 X^2+2  1  X  1 X^2+2  1 X^2+X
 0  1  0  0 X^2+1 X^2+X+1  1 X^2+X  1  1 X+2 X+1 X^2  1 X^2+2  2 X+2 X^2+X+3  1  1  1  1  1 X+2 X^2+X+2  1 X^2+X X^2+X+1  2  1 X^2+X X+2  3  X  1  1
 0  0  1  1  1  0 X^2+X+1  3 X^2+1  X X^2+X+2  2  1 X+1  1  0  1 X^2+X+1  3 X+2 X^2+2 X^2+X+2 X+1 X^2+X+1 X+3 X^2+X X^2 X+1  1 X^2+X+2  1  1 X^2+X  2 X+1  0
 0  0  0  X X+2 X+2 X^2+X  X X^2+2 X+2 X^2+X+2 X^2+2 X^2+X+2 X^2+2  2 X^2+X+2 X^2+2 X^2+2  2  2 X^2+X  2  X  2 X^2+X X^2+X+2  0  2 X^2+2 X^2  2 X+2 X^2+X  X  X  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+440x^31+1138x^32+2656x^33+3614x^34+5790x^35+5594x^36+5876x^37+3506x^38+2590x^39+987x^40+392x^41+118x^42+42x^43+16x^44+4x^45+2x^46+2x^47

The gray image is a code over GF(2) with n=288, k=15 and d=124.
This code was found by Heurico 1.16 in 10.7 seconds.