The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+82x^11+128x^12+242x^13+152x^14+236x^15+75x^16+76x^17+24x^18+2x^19+4x^20+2x^21

The gray image is a code over GF(2) with n=56, k=10 and d=22.
This code was found by Heurico 1.11 in 0.0242 seconds.