The generator matrix

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

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+17x^12+46x^13+28x^14+4x^15+14x^16+14x^17+3x^18+1x^22

The gray image is a code over GF(2) with n=56, k=7 and d=24.
This code was found by Heurico 1.16 in 0.000768 seconds.