The generator matrix

 1  0  0  0  1  1  1  1  2  0  1  X  1  1
 0  1  0  0  0  2 X+1  3  1  1 X+2  1  2 X+2
 0  0  1  0  1  X X+2 X+1 X+1  0  3  X X+3 X+2
 0  0  0  1  1 X+1  X X+3  X X+1 X+2  0  X  3
 0  0  0  0  2  0  0  0  0  2  2  0  2  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+294x^10+452x^11+962x^12+1568x^13+1558x^14+1672x^15+1031x^16+384x^17+226x^18+20x^19+22x^20+2x^22

The gray image is a code over GF(2) with n=56, k=13 and d=20.
This code was found by Heurico 1.13 in 0.129 seconds.