The generator matrix

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

generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+198x^83+811x^84+1258x^85+1719x^86+1888x^87+2122x^88+1802x^89+1724x^90+1218x^91+1189x^92+828x^93+635x^94+426x^95+247x^96+134x^97+103x^98+40x^99+20x^100+8x^101+2x^102+6x^103+1x^106+2x^108+2x^109

The gray image is a code over GF(2) with n=712, k=14 and d=332.
This code was found by Heurico 1.16 in 4.22 seconds.