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

generates a code of length 88 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+63x^84+4x^85+84x^86+188x^87+364x^88+188x^89+64x^90+4x^91+44x^92+12x^94+6x^96+1x^100+1x^160

The gray image is a linear code over GF(2) with n=704, k=10 and d=336.
This code was found by Heurico 1.16 in 0.61 seconds.