The generator matrix

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

generates a code of length 92 over Z2[X]/(X^4) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+862x^85+2042x^86+3322x^87+4430x^88+5642x^89+6123x^90+7488x^91+6908x^92+7256x^93+6216x^94+4910x^95+3912x^96+2926x^97+1541x^98+1076x^99+430x^100+262x^101+102x^102+36x^103+23x^104+12x^105+6x^106+8x^108+2x^110

The gray image is a linear code over GF(2) with n=736, k=16 and d=340.
This code was found by Heurico 1.16 in 139 seconds.