The generator matrix

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

generates a code of length 17 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+188x^12+1058x^13+4325x^14+12604x^15+28161x^16+38174x^17+28481x^18+12712x^19+4156x^20+958x^21+215x^22+28x^23+6x^24+2x^25+3x^26

The gray image is a code over GF(2) with n=136, k=17 and d=48.
This code was found by Heurico 1.16 in 22.3 seconds.