The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+32x^6+109x^8+224x^10+512x^11+392x^12+1536x^13+2560x^14+1536x^15+427x^16+512x^17+224x^18+88x^20+32x^22+7x^24

The gray image is a code over GF(2) with n=56, k=13 and d=12.
This code was found by Heurico 1.16 in 0.125 seconds.