The generator matrix

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

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+38x^9+100x^10+192x^11+482x^12+782x^13+877x^14+818x^15+500x^16+186x^17+78x^18+28x^19+8x^20+2x^21+1x^22+2x^23+1x^24

The gray image is a code over GF(2) with n=56, k=12 and d=18.
This code was found by Heurico 1.16 in 0.0738 seconds.