The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  1  1  1
 0  2  0  0  0  0  0  0  0  2  0  2  2  0
 0  0  2  0  0  0  0  0  0  2  2  2  0  0
 0  0  0  2  0  0  0  0  0  2  2  0  2  0
 0  0  0  0  2  0  0  0  2  2  0  0  2  0
 0  0  0  0  0  2  0  0  2  0  0  2  2  0
 0  0  0  0  0  0  2  0  2  0  2  2  0  0
 0  0  0  0  0  0  0  2  2  2  2  0  0  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+38x^8+17x^10+52x^12+128x^13+556x^14+128x^15+33x^16+54x^18+4x^20+12x^22+1x^26

The gray image is a code over GF(2) with n=56, k=10 and d=16.
This code was found by Heurico 1.16 in 0.00423 seconds.