The generator matrix

 1  1  1  1  X  1  1  0  X  1  1  X  X  1
 0  X  0 X+2  X  0 X+2  X X+2  0 X+2 X+2  0  0
 0  0  2  0  0  0  0  0  0  2  0  2  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  0  0  2  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  0  2  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+46x^8+16x^9+49x^10+144x^11+108x^12+608x^13+108x^14+608x^15+89x^16+144x^17+86x^18+16x^19+12x^20+12x^22+1x^26

The gray image is a code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0136 seconds.