The generator matrix

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

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+188x^85+732x^86+664x^87+576x^88+390x^89+477x^90+296x^91+240x^92+166x^93+116x^94+76x^95+61x^96+36x^97+64x^98+8x^99+1x^100+2x^102+1x^110+1x^112

The gray image is a linear code over GF(2) with n=712, k=12 and d=340.
This code was found by Heurico 1.16 in 0.5 seconds.