The generator matrix

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

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+103x^10+292x^11+512x^12+720x^13+795x^14+776x^15+555x^16+240x^17+77x^18+20x^19+4x^20+1x^22

The gray image is a code over GF(2) with n=56, k=12 and d=20.
This code was found by Heurico 1.11 in 0.0341 seconds.