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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+33x^66+58x^68+81x^70+128x^71+117x^72+1280x^73+104x^74+128x^75+58x^76+17x^78+7x^80+7x^82+4x^84+9x^86+9x^88+5x^94+1x^96+1x^128

The gray image is a linear code over GF(2) with n=584, k=11 and d=264.
This code was found by Heurico 1.16 in 96.4 seconds.