The generator matrix

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

generates a code of length 74 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+148x^69+198x^70+512x^71+516x^72+440x^73+575x^74+482x^75+397x^76+440x^77+194x^78+114x^79+25x^80+28x^81+8x^82+4x^83+2x^84+6x^87+2x^88+2x^91+1x^106+1x^108

The gray image is a code over GF(2) with n=592, k=12 and d=276.
This code was found by Heurico 1.16 in 0.625 seconds.