The generator matrix

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

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+262x^12+422x^14+239x^16+42x^18+10x^20+2x^22

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 0.00612 seconds.