The generator matrix

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

generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+154x^68+614x^69+694x^70+700x^71+456x^72+422x^73+299x^74+228x^75+170x^76+164x^77+69x^78+52x^79+41x^80+28x^81+1x^82+1x^84+1x^88+1x^90

The gray image is a linear code over GF(2) with n=576, k=12 and d=272.
This code was found by Heurico 1.16 in 2.72 seconds.