The generator matrix

 1  1  1  1  1  1  1  1  X  X  1  1  X  1
 0  X  0  0  0  0  0  2 X+2 X+2 X+2 X+2  2  X
 0  0  X  0  0  2 X+2  X X+2  0  X  X  2  X
 0  0  0  X  0 X+2 X+2  X  0  2  2  X  X  0
 0  0  0  0  X  X  2 X+2 X+2  0 X+2  X  X  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+28x^9+79x^10+114x^11+190x^12+374x^13+475x^14+372x^15+215x^16+104x^17+53x^18+26x^19+10x^20+6x^21+1x^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 0.0404 seconds.