The generator matrix

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

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+46x^10+154x^11+202x^12+430x^13+396x^14+416x^15+207x^16+144x^17+38x^18+6x^19+6x^20+2x^21

The gray image is a code over GF(2) with n=56, k=11 and d=20.
This code was found by Heurico 1.16 in 0.0185 seconds.