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

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+68x^84+72x^85+82x^86+32x^87+488x^88+560x^89+500x^90+32x^91+72x^92+72x^93+58x^94+10x^96+1x^176

The gray image is a linear code over GF(2) with n=712, k=11 and d=336.
This code was found by Heurico 1.16 in 0.938 seconds.