The generator matrix

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

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+40x^6+192x^7+295x^8+192x^9+216x^10+640x^11+5040x^12+640x^13+216x^14+192x^15+295x^16+192x^17+40x^18+1x^24

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 0.147 seconds.