The generator matrix

 1  0  0  1  1  1  X  0  1  2  1  1  1  1
 0  1  0  1  0  1  1  1 X+1  1 X+3  2  X  0
 0  0  1  1 X+1  X  1  0 X+2  3  3 X+3  1  0
 0  0  0  X  X  2  0  X  X  2  2  2  0  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+31x^10+176x^11+228x^12+386x^13+386x^14+440x^15+207x^16+140x^17+39x^18+8x^19+4x^20+2x^21

The gray image is a code over GF(2) with n=56, k=11 and d=20.
This code was found by Heurico 1.11 in 0.00893 seconds.