The generator matrix

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

generates a code of length 74 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+220x^66+1434x^67+2840x^68+5018x^69+7123x^70+11408x^71+12567x^72+16860x^73+15821x^74+17332x^75+12954x^76+11410x^77+7101x^78+4708x^79+2285x^80+1138x^81+433x^82+240x^83+70x^84+68x^85+20x^86+10x^87+3x^88+2x^89+2x^90+2x^91+2x^95

The gray image is a code over GF(2) with n=592, k=17 and d=264.
This code was found by Heurico 1.16 in 163 seconds.