The generator matrix

 1  0  1  1  1 X+2  1  2  1  1  2  1  X  1
 0  1  1 X+2 X+3  1  2  1 X+1  X  1 X+1  0 X+1
 0  0  X  0 X+2  2  X  X  0 X+2 X+2  2  0  0
 0  0  0  2  0  2  0  2  0  2  0  0  2  0
 0  0  0  0  2  0  2  0  2  0  2  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+26x^10+78x^11+64x^12+314x^13+76x^14+300x^15+59x^16+68x^17+26x^18+6x^19+4x^20+2x^21

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 0.00661 seconds.