The generator matrix

 1  0  1  1  1  0  1  1  1  1
 0  1 X+1 X+2  1  1  0  0  0  0
 0  0  2  0  0  0  0  2  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  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+29x^4+32x^5+24x^6+64x^7+194x^8+416x^9+528x^10+416x^11+194x^12+64x^13+24x^14+32x^15+29x^16+1x^20

The gray image is a code over GF(2) with n=40, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00282 seconds.