The generator matrix

 1  0  1  1  1  2  1  1  1 X+2  2  1  X  1
 0  1  1  0 X+1  1  0 X+1  X  1  1  X  1  0
 0  0  X  0  X  2  X  2 X+2  0  0  0  X  2
 0  0  0  X  X X+2 X+2  2  0  2  X  0  2  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+20x^10+46x^11+163x^12+154x^13+277x^14+140x^15+153x^16+36x^17+22x^18+6x^19+3x^20+2x^21+1x^22

The gray image is a code over GF(2) with n=56, k=10 and d=20.
This code was found by Heurico 1.16 in 0.00689 seconds.