The generator matrix
1 1 1 1 X X X 1
0 X^3+X^2 0 X^2 0 X^2 X^3+X^2 0
0 0 X^3+X^2 X^2 X^3+X^2 X^2 0 0
0 0 0 X^3 0 0 X^3 0
0 0 0 0 X^3 0 X^3 0
0 0 0 0 0 X^3 X^3 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+39x^4+32x^5+150x^6+96x^7+1407x^8+96x^9+164x^10+32x^11+25x^12+6x^14
The gray image is a linear code over GF(2) with n=64, k=11 and d=16.
This code was found by Heurico 1.16 in 0.016 seconds.