The generator matrix

 1  0  1  1  1  0  X  X  1  1
 0  1  1  0 X+1  1  0  0  0  0
 0  0  X X+2  0 X+2  X  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  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+61x^4+216x^6+32x^7+674x^8+480x^9+1168x^10+480x^11+674x^12+32x^13+216x^14+61x^16+1x^20

The gray image is a code over GF(2) with n=40, k=12 and d=8.
This code was found by Heurico 1.16 in 0.00943 seconds.