The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+15x^10+34x^11+54x^12+98x^13+123x^14+92x^15+39x^16+28x^17+21x^18+2x^19+2x^20+2x^21+1x^22

The gray image is a code over GF(2) with n=56, k=9 and d=20.
This code was found by Heurico 1.16 in 0.00298 seconds.