The generator matrix

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

generates a code of length 97 over Z2[X]/(X^4) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+230x^90+1120x^91+1669x^92+2552x^93+2995x^94+3238x^95+3323x^96+3704x^97+3141x^98+2980x^99+2420x^100+2184x^101+1225x^102+814x^103+514x^104+316x^105+158x^106+72x^107+43x^108+24x^109+18x^110+16x^111+6x^112+4x^113+1x^114

The gray image is a linear code over GF(2) with n=776, k=15 and d=360.
This code was found by Heurico 1.16 in 21.6 seconds.