The generator matrix

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

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+704x^83+2290x^84+2970x^85+4493x^86+5436x^87+6738x^88+6914x^89+7464x^90+7068x^91+6309x^92+4876x^93+4249x^94+2502x^95+1819x^96+860x^97+455x^98+208x^99+79x^100+66x^101+10x^102+2x^103+4x^104+10x^105+9x^106

The gray image is a linear code over GF(2) with n=720, k=16 and d=332.
This code was found by Heurico 1.16 in 56 seconds.