The generator matrix

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

generates a code of length 18 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+148x^13+1291x^14+4642x^15+13363x^16+27846x^17+36099x^18+28372x^19+13646x^20+4256x^21+1105x^22+266x^23+28x^24+6x^25+1x^26+2x^28

The gray image is a code over GF(2) with n=144, k=17 and d=52.
This code was found by Heurico 1.16 in 24.9 seconds.