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

generates a code of length 76 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+21x^68+40x^70+44x^72+32x^73+36x^74+608x^75+539x^76+608x^77+19x^78+32x^79+15x^80+10x^82+9x^84+10x^86+4x^88+10x^90+7x^92+2x^94+1x^142

The gray image is a linear code over GF(2) with n=608, k=11 and d=272.
This code was found by Heurico 1.16 in 0.453 seconds.