The generator matrix

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

generates a code of length 12 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+37x^6+32x^7+174x^8+480x^9+856x^10+1536x^11+1956x^12+1536x^13+866x^14+480x^15+169x^16+32x^17+32x^18+4x^20+1x^22

The gray image is a code over GF(2) with n=48, k=13 and d=12.
This code was found by Heurico 1.16 in 0.0827 seconds.