The generator matrix

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

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+88x^10+308x^11+502x^12+726x^13+856x^14+720x^15+519x^16+276x^17+80x^18+12x^19+2x^20+6x^21

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 0.0722 seconds.