The generator matrix

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

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+36x^9+63x^10+120x^11+260x^12+348x^13+389x^14+368x^15+243x^16+124x^17+57x^18+24x^19+8x^20+4x^21+3x^22

The gray image is a code over GF(2) with n=56, k=11 and d=18.
This code was found by Heurico 1.16 in 0.0237 seconds.