The generator matrix

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

generates a code of length 74 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+274x^67+1488x^68+2952x^69+3882x^70+5554x^71+6820x^72+8202x^73+8034x^74+7828x^75+6862x^76+5328x^77+3670x^78+2344x^79+1192x^80+620x^81+243x^82+154x^83+52x^84+16x^85+10x^86+6x^87+1x^88+2x^89+1x^90

The gray image is a code over GF(2) with n=592, k=16 and d=268.
This code was found by Heurico 1.16 in 39.6 seconds.