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

generates a code of length 96 over Z2[X]/(X^4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+92x^88+1056x^89+2017x^90+3322x^91+4322x^92+5810x^93+6074x^94+7220x^95+7073x^96+6768x^97+6005x^98+5450x^99+3863x^100+2782x^101+1453x^102+1138x^103+557x^104+284x^105+110x^106+52x^107+32x^108+20x^109+13x^110+18x^111+3x^112+1x^116

The gray image is a linear code over GF(2) with n=768, k=16 and d=352.
This code was found by Heurico 1.16 in 54.4 seconds.