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

generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+156x^83+61x^84+176x^85+322x^86+660x^87+340x^88+148x^89+28x^90+100x^91+11x^92+24x^93+2x^94+12x^95+2x^96+4x^97+1x^168

The gray image is a linear code over GF(2) with n=696, k=11 and d=332.
This code was found by Heurico 1.16 in 0.844 seconds.