The generator matrix

 1  0  0  1  1  1  X  1  1  1  1
 0  1  0  1 X+2 X+3  1  0  0  0  0
 0  0  1  1 X+3 X+2  1  0  0  0  0
 0  0  0  2  0  0  0  0  2  0  0
 0  0  0  0  2  0  0  0  2  0  0
 0  0  0  0  0  2  0  0  2  0  0
 0  0  0  0  0  0  2  0  2  0  0
 0  0  0  0  0  0  0  2  2  0  0

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+68x^4+128x^5+224x^6+384x^7+574x^8+2176x^9+1160x^10+6912x^11+1244x^12+2176x^13+496x^14+384x^15+281x^16+128x^17+40x^18+8x^20

The gray image is a code over GF(2) with n=44, k=14 and d=8.
This code was found by Heurico 1.16 in 0.147 seconds.