The generator matrix

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

generates a code of length 98 over Z2[X]/(X^4) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+268x^91+1019x^92+1854x^93+2324x^94+2962x^95+3103x^96+3804x^97+3325x^98+3580x^99+2985x^100+2374x^101+1677x^102+1430x^103+910x^104+532x^105+282x^106+134x^107+64x^108+60x^109+46x^110+4x^111+4x^112+16x^113+1x^114+6x^115+2x^116+1x^118

The gray image is a linear code over GF(2) with n=784, k=15 and d=364.
This code was found by Heurico 1.16 in 23.9 seconds.