The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+398x^75+1725x^76+3302x^77+5257x^78+8290x^79+10935x^80+13628x^81+14515x^82+15360x^83+14942x^84+13746x^85+10531x^86+7828x^87+4938x^88+2890x^89+1505x^90+706x^91+347x^92+128x^93+44x^94+26x^95+21x^96+2x^97+4x^98+2x^100+1x^112

The gray image is a code over GF(2) with n=664, k=17 and d=300.
This code was found by Heurico 1.16 in 206 seconds.