The generator matrix

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

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+868x^83+1856x^84+3344x^85+4200x^86+5726x^87+6322x^88+7618x^89+6983x^90+7456x^91+5840x^92+5396x^93+3607x^94+2898x^95+1565x^96+1002x^97+469x^98+192x^99+100x^100+40x^101+21x^102+12x^103+12x^104+8x^105

The gray image is a code over GF(2) with n=720, k=16 and d=332.
This code was found by Heurico 1.16 in 56.5 seconds.