The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+154x^83+966x^84+1228x^85+1788x^86+1622x^87+2046x^88+1762x^89+2004x^90+1260x^91+1144x^92+768x^93+722x^94+340x^95+294x^96+118x^97+86x^98+26x^99+20x^100+8x^101+14x^102+6x^103+1x^104+4x^105+2x^106

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 4.69 seconds.