The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+84x^69+628x^70+1358x^71+2381x^72+2726x^73+3623x^74+3988x^75+4176x^76+3492x^77+3501x^78+2440x^79+1984x^80+1132x^81+685x^82+300x^83+113x^84+58x^85+41x^86+26x^87+14x^88+10x^89+3x^92+2x^93+2x^94

The gray image is a code over GF(2) with n=608, k=15 and d=276.
This code was found by Heurico 1.16 in 12.2 seconds.