The generator matrix

 1  0  1  1  1  0  1  1  2  1  1 X+2  1  1
 0  1  1  0 X+1  1 X+1  0  1  X X+2  1 X+3  2
 0  0  X  0  0  0  X X+2  X  X  2 X+2  X  0
 0  0  0  X  0 X+2  X  X  2  0  2 X+2  0 X+2
 0  0  0  0  2  0  0  2  2  2  2  0  2  0
 0  0  0  0  0  2  0  0  0  2  2  2  0  2

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+44x^9+79x^10+224x^11+388x^12+1004x^13+613x^14+1024x^15+371x^16+228x^17+73x^18+32x^19+8x^20+4x^21+3x^22

The gray image is a code over GF(2) with n=56, k=12 and d=18.
This code was found by Heurico 1.16 in 0.674 seconds.