The generator matrix

 1  1  1  1  X  1  1  0  X  X  1  1  1  1
 0  X  0 X+2  X  0 X+2  X X+2 X+2  2 X+2  0  0
 0  0  2  0  0  0  0  0  2  2  2  0  0  0
 0  0  0  2  0  0  0  0  2  2  0  2  0  0
 0  0  0  0  2  0  0  2  2  2  0  0  0  0
 0  0  0  0  0  2  0  2  2  0  2  0  0  0
 0  0  0  0  0  0  2  2  0  2  0  2  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+26x^8+48x^10+32x^11+165x^12+224x^13+32x^14+224x^15+165x^16+32x^17+48x^18+26x^20+1x^28

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 0.00502 seconds.