The generator matrix
1 1 1 1 X X 1 1
0 X 0 X^3+X^2+X X^2+X X^2+X X^3 0
0 0 X^3+X^2 0 0 X^2 X^3 0
0 0 0 X^3+X^2 0 X^2 X^3+X^2 X^3
0 0 0 0 X^3 X^3 0 0
generates a code of length 8 over Z2[X]/(X^4) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+28x^4+48x^5+224x^6+720x^7+2054x^8+720x^9+224x^10+48x^11+28x^12+1x^16
The gray image is a linear code over GF(2) with n=64, k=12 and d=16.
This code was found by Heurico 1.16 in 0.016 seconds.