The generator matrix

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

generates a code of length 18 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+678x^14+2310x^15+7084x^16+13520x^17+18100x^18+13938x^19+7166x^20+2012x^21+622x^22+86x^23+13x^24+4x^25+2x^27

The gray image is a code over GF(2) with n=144, k=16 and d=56.
This code was found by Heurico 1.16 in 6.97 seconds.