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

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+119x^74+158x^76+537x^78+512x^79+516x^80+80x^82+55x^84+46x^86+3x^88+13x^90+2x^92+5x^94+1x^140

The gray image is a linear code over GF(2) with n=632, k=11 and d=296.
This code was found by Heurico 1.16 in 10.5 seconds.