The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+8x^13+44x^14+8x^15+1x^16+2x^20

The gray image is a code over GF(2) with n=56, k=6 and d=26.
This code was found by Heurico 1.16 in 0.000395 seconds.