The generator matrix

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

generates a code of length 7 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+55x^2+88x^3+469x^4+1440x^5+3571x^6+5136x^7+3571x^8+1440x^9+469x^10+88x^11+55x^12+1x^14

The gray image is a code over GF(2) with n=28, k=14 and d=4.
This code was found by Heurico 1.16 in 0.0738 seconds.