The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+210x^83+857x^84+1278x^85+1670x^86+1852x^87+2062x^88+1772x^89+1570x^90+1410x^91+1311x^92+898x^93+609x^94+324x^95+258x^96+134x^97+82x^98+40x^99+16x^100+12x^101+4x^102+4x^103+7x^104+1x^110+2x^113

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 4.73 seconds.