The generator matrix

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

generates a code of length 88 over Z2[X]/(X^4) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+217x^82+734x^83+1468x^84+1516x^85+2041x^86+1718x^87+2165x^88+1292x^89+1773x^90+1000x^91+1030x^92+542x^93+336x^94+226x^95+121x^96+108x^97+45x^98+18x^99+14x^100+14x^101+3x^102+1x^104+1x^106

The gray image is a linear code over GF(2) with n=704, k=14 and d=328.
This code was found by Heurico 1.16 in 20.6 seconds.