The generator matrix

 1  1  1  1  1  1  1  X  X  X  1  1  1  1
 0  2  0  2  0  0  2  0  2  2  2  0  0  2
 0  0  2  2  0  2  2  2  2  0  0  0  2  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+6x^13+19x^14+3x^16+2x^17+1x^22

The gray image is a code over GF(2) with n=56, k=5 and d=26.
This code was found by Heurico 1.16 in 0.000516 seconds.