The generator matrix

 1  0  1  1  1  X  1  1  1  1  2 X+2  0  0
 0  1  1  2 X+1  1  X X+3 X+2  3  X  1  0  1
 0  0  X X+2  2 X+2  X X+2  2  0 X+2 X+2  X  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+50x^12+96x^13+32x^14+39x^16+32x^17+6x^20

The gray image is a code over GF(2) with n=56, k=8 and d=24.
This code was found by Heurico 1.16 in 0.00116 seconds.