The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+131x^10+208x^11+561x^12+696x^13+910x^14+696x^15+581x^16+168x^17+111x^18+24x^19+9x^20

The gray image is a code over GF(2) with n=56, k=12 and d=20.
This code was found by Heurico 1.16 in 0.104 seconds.