The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+11x^14+42x^15+41x^16+166x^17+526x^18+492x^19+524x^20+148x^21+36x^22+42x^23+6x^24+6x^25+2x^26+4x^28+1x^30

The gray image is a code over GF(2) with n=152, k=11 and d=56.
This code was found by Heurico 1.16 in 0.016 seconds.