The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+60x^71+777x^72+880x^73+1250x^74+1072x^75+1116x^76+772x^77+612x^78+492x^79+476x^80+228x^81+267x^82+52x^83+76x^84+24x^85+30x^86+4x^87+1x^90+2x^92

The gray image is a code over GF(2) with n=608, k=13 and d=284.
This code was found by Heurico 1.16 in 1 seconds.