The generator matrix

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

generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+156x^83+949x^84+1640x^85+2352x^86+2932x^87+3322x^88+3820x^89+3698x^90+3352x^91+3175x^92+2368x^93+1848x^94+1456x^95+777x^96+368x^97+302x^98+124x^99+48x^100+24x^101+16x^102+12x^103+22x^104+4x^105+2x^108

The gray image is a linear code over GF(2) with n=720, k=15 and d=332.
This code was found by Heurico 1.16 in 21.7 seconds.