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

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+148x^85+67x^86+212x^87+378x^88+496x^89+400x^90+148x^91+34x^92+108x^93+11x^94+20x^95+2x^96+16x^97+2x^98+4x^99+1x^168

The gray image is a linear code over GF(2) with n=712, k=11 and d=340.
This code was found by Heurico 1.16 in 0.906 seconds.