The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1
 0  X  0 X+2  0  2 X+2 X+2  0 X+2 X+2  2  0  0
 0  0  2  0  0  2  0  0  0  2  2  0  2  0
 0  0  0  2  0  0  0  2  2  2  0  2  2  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  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+9x^10+8x^11+18x^12+56x^13+76x^14+56x^15+11x^16+8x^17+10x^18+2x^20+1x^26

The gray image is a code over GF(2) with n=56, k=8 and d=20.
This code was found by Heurico 1.16 in 0.00143 seconds.