The generator matrix

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

generates a code of length 93 over Z2[X]/(X^4) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+108x^85+1020x^86+2038x^87+3406x^88+4480x^89+5424x^90+5938x^91+7347x^92+6870x^93+7100x^94+5946x^95+5676x^96+3808x^97+2754x^98+1562x^99+1049x^100+584x^101+196x^102+88x^103+53x^104+48x^105+18x^106+12x^107+4x^108+6x^109

The gray image is a linear code over GF(2) with n=744, k=16 and d=340.
This code was found by Heurico 1.16 in 53.5 seconds.