The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  X  X
 0  X  0  0  0  X X+2  X  0  2  2  X  X  2
 0  0  X  0  X  X  X  2  0  2  0  X X+2 X+2
 0  0  0  X  X  2 X+2 X+2  0 X+2  X  0  2 X+2
 0  0  0  0  2  2  2  2  2  2  2  2  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+37x^10+82x^11+131x^12+176x^13+186x^14+180x^15+113x^16+64x^17+33x^18+10x^19+11x^20

The gray image is a code over GF(2) with n=56, k=10 and d=20.
This code was found by Heurico 1.16 in 0.00882 seconds.