The generator matrix

 1  0  1  1  1  0  X  X  X  1
 0  1  1  0 X+1  1  0  0  0  0
 0  0  X  0  X  0  X  X  0  0
 0  0  0  X  X X+2  X  0  0  0
 0  0  0  0  2  0  0  0  2  0
 0  0  0  0  0  2  0  0  2  0
 0  0  0  0  0  0  2  0  2  0
 0  0  0  0  0  0  0  2  2  0

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+100x^4+56x^5+520x^6+728x^7+1854x^8+3312x^9+3256x^10+3312x^11+1812x^12+728x^13+568x^14+56x^15+73x^16+8x^18

The gray image is a code over GF(2) with n=40, k=14 and d=8.
This code was found by Heurico 1.16 in 0.171 seconds.