The generator matrix

 1  0  0  0  1  1  1  1  2  0  1  1 X+2  1
 0  1  0  0  0  2 X+1  3  1  1  3  X  X  2
 0  0  1  0  1  X X+2 X+1 X+1  0  3  X X+2 X+1
 0  0  0  1  1 X+1  X X+3  X X+1 X+1  0  1 X+1
 0  0  0  0  2  0  0  0  0  2  2  2  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+280x^10+476x^11+1018x^12+1400x^13+1725x^14+1552x^15+1100x^16+392x^17+202x^18+20x^19+24x^20+1x^22+1x^24

The gray image is a code over GF(2) with n=56, k=13 and d=20.
This code was found by Heurico 1.16 in 1.05 seconds.