The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+6x^12+24x^13+6x^14+16x^15+1x^16+8x^17+2x^18

The gray image is a code over GF(2) with n=56, k=6 and d=24.
This code was found by Heurico 1.16 in 0.00075 seconds.