The generator matrix

 1  0  0  1  1  1  X  1  X  2  2  1  1  1
 0  1  0  1  0 X+3  1  X  0  X  0  0 X+3  2
 0  0  1  1  1  0  1  X  1  1  1  1  X  2
 0  0  0  X  0 X+2  0  X  2 X+2  X X+2  2  0
 0  0  0  0  X  0  2  X X+2  X  2  2  0  0
 0  0  0  0  0  2  2  0  2  0  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+32x^8+144x^9+403x^10+724x^11+1865x^12+3292x^13+3539x^14+3080x^15+1978x^16+840x^17+337x^18+100x^19+27x^20+12x^21+9x^22+1x^24

The gray image is a code over GF(2) with n=56, k=14 and d=16.
This code was found by Heurico 1.16 in 0.755 seconds.