The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  2  1  X
 0  X  0  X  0  0  X X+2  2  2  X  X  X X+2
 0  0  X  X  0 X+2  X  2  0  X  X X+2  X  0
 0  0  0  2  0  0  2  0  0  2  0  2  0  2
 0  0  0  0  2  0  0  2  2  2  0  0  0  2
 0  0  0  0  0  2  2  0  2  0  0  2  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+62x^10+16x^11+198x^12+112x^13+262x^14+112x^15+175x^16+16x^17+58x^18+10x^20+2x^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 0.126 seconds.