The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+262x^67+1388x^68+2774x^69+4405x^70+5202x^71+7600x^72+7510x^73+8100x^74+7410x^75+7215x^76+5304x^77+3862x^78+2118x^79+1371x^80+526x^81+273x^82+88x^83+71x^84+30x^85+15x^86+8x^87+2x^88+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 43.9 seconds.