The generator matrix

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

generates a code of length 19 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+260x^14+1378x^15+5093x^16+13218x^17+28174x^18+34612x^19+28346x^20+13636x^21+4800x^22+1130x^23+382x^24+26x^25+14x^26+2x^28

The gray image is a code over GF(2) with n=152, k=17 and d=56.
This code was found by Heurico 1.16 in 26.2 seconds.