The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+125x^8+512x^10+1912x^12+3072x^14+1947x^16+512x^18+104x^20+7x^24

The gray image is a code over GF(2) with n=56, k=13 and d=16.
This code was found by Heurico 1.16 in 0.198 seconds.