The generator matrix
1 1 1 1 X X 1
0 X 0 X X^2 X^3+X^2 X^2+X
0 0 X X X X 0
0 0 0 X^2 0 X^3+X^2 X^3
generates a code of length 7 over Z2[X]/(X^4) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+60x^4+256x^5+696x^6+2056x^7+729x^8+240x^9+48x^10+8x^11+2x^12
The gray image is a linear code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.016 seconds.