The generator matrix

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

generates a code of length 90 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+162x^83+967x^84+1712x^85+2261x^86+2678x^87+3575x^88+3664x^89+3874x^90+3240x^91+3494x^92+2318x^93+1876x^94+1192x^95+742x^96+430x^97+273x^98+126x^99+69x^100+66x^101+13x^102+26x^103+2x^105+7x^106

The gray image is a code over GF(2) with n=720, k=15 and d=332.
This code was found by Heurico 1.16 in 14.6 seconds.