The generator matrix

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

generates a code of length 8 over Z2[X]/(X^4) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+48x^5+196x^6+754x^7+2105x^8+750x^9+188x^10+46x^11+6x^12+2x^13

The gray image is a linear code over GF(2) with n=64, k=12 and d=20.
This code was found by Heurico 1.16 in 0.015 seconds.