The generator matrix

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

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+212x^83+811x^84+1266x^85+1740x^86+1912x^87+2073x^88+1690x^89+1715x^90+1234x^91+1220x^92+898x^93+657x^94+424x^95+287x^96+102x^97+38x^98+54x^99+21x^100+12x^101+6x^102+4x^103+3x^104+3x^106+1x^110

The gray image is a linear code over GF(2) with n=712, k=14 and d=332.
This code was found by Heurico 1.16 in 11 seconds.