The generator matrix

 1  0  1  1  1 X+2  1  1  1  0  1  2  X  2
 0  1  1 X+2 X+3  1  2 X+1  X  1 X+3  1  1  1
 0  0  X  0 X+2  0  X  0  X  2 X+2  X X+2 X+2
 0  0  0  2  0  0  2  0  2  2  2  0  2  0
 0  0  0  0  2  0  2  2  0  0  0  2  0  2
 0  0  0  0  0  2  0  2  0  2  0  2  2  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+70x^10+48x^11+390x^12+208x^13+630x^14+208x^15+367x^16+48x^17+66x^18+10x^20+2x^22

The gray image is a code over GF(2) with n=56, k=11 and d=20.
This code was found by Heurico 1.16 in 0.067 seconds.