The generator matrix

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

generates a code of length 97 over Z2[X]/(X^4) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+270x^91+843x^92+1468x^93+1743x^94+1788x^95+1745x^96+1890x^97+1469x^98+1540x^99+1051x^100+860x^101+677x^102+364x^103+271x^104+194x^105+89x^106+46x^107+34x^108+20x^109+5x^110+8x^111+4x^112+2x^116+1x^118+1x^120

The gray image is a linear code over GF(2) with n=776, k=14 and d=364.
This code was found by Heurico 1.16 in 12.6 seconds.