The generator matrix

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

generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+16x^74+28x^75+44x^76+34x^77+72x^78+104x^79+581x^80+406x^81+544x^82+76x^83+12x^84+30x^85+8x^86+32x^87+1x^88+26x^89+16x^91+16x^93+1x^152

The gray image is a linear code over GF(2) with n=648, k=11 and d=296.
This code was found by Heurico 1.16 in 0.719 seconds.