The generator matrix

 1  0  0  1  1  1  X  X  1  1
 0  1  0  1 X+2 X+3  1  0  0  0
 0  0  1  1 X+3 X+2  1  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+128x^5+216x^6+320x^7+1250x^8+576x^9+3088x^10+576x^11+1250x^12+320x^13+216x^14+128x^15+61x^16+1x^20

The gray image is a code over GF(2) with n=40, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0331 seconds.