The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1  1  1  1
 0  1 X+1 X+2  1  1  0 X+1  1  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  2  0  2  2
 0  0  0  0  0  2  0  0  0  0  2  0  0  2
 0  0  0  0  0  0  2  0  0  0  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  2  2  0  2
 0  0  0  0  0  0  0  0  2  0  0  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+16x^7+109x^8+112x^9+224x^10+592x^11+1416x^12+4400x^13+2560x^14+4400x^15+1451x^16+592x^17+224x^18+112x^19+88x^20+16x^21+32x^22+7x^24

The gray image is a code over GF(2) with n=56, k=14 and d=12.
This code was found by Heurico 1.16 in 0.275 seconds.