The generator matrix

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

generates a code of length 36 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+174x^29+1095x^30+3460x^31+8037x^32+17652x^33+31102x^34+42960x^35+51990x^36+44464x^37+31555x^38+17432x^39+7686x^40+3084x^41+1037x^42+272x^43+90x^44+34x^45+10x^46+4x^47+4x^48+1x^50

The gray image is a code over GF(2) with n=288, k=18 and d=116.
This code was found by Heurico 1.16 in 262 seconds.