The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+160x^14+992x^15+2789x^16+6692x^17+13932x^18+16268x^19+14072x^20+6944x^21+2576x^22+816x^23+258x^24+28x^25+4x^26+4x^27

The gray image is a code over GF(2) with n=152, k=16 and d=56.
This code was found by Heurico 1.16 in 7.42 seconds.