The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+206x^68+1300x^69+3149x^70+5074x^71+7972x^72+10764x^73+13274x^74+15386x^75+16373x^76+16120x^77+14057x^78+10430x^79+7644x^80+4712x^81+2432x^82+1236x^83+555x^84+188x^85+112x^86+56x^87+16x^88+4x^89+8x^91+1x^96+2x^99

The gray image is a code over GF(2) with n=608, k=17 and d=272.
This code was found by Heurico 1.16 in 180 seconds.