The generator matrix

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

generates a code of length 74 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+38x^70+314x^71+379x^72+300x^73+167x^74+310x^75+170x^76+200x^77+65x^78+32x^79+29x^80+24x^81+8x^82+4x^83+1x^84+4x^88+1x^94+1x^102

The gray image is a code over GF(2) with n=592, k=11 and d=280.
This code was found by Heurico 1.16 in 0.328 seconds.