The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+230x^9+820x^10+1924x^11+3801x^12+5974x^13+7072x^14+6184x^15+3986x^16+1826x^17+652x^18+244x^19+51x^20+2x^21+1x^24

The gray image is a code over GF(2) with n=56, k=15 and d=18.
This code was found by Heurico 1.13 in 1.48 seconds.