The generator matrix

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

generates a code of length 73 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+346x^70+308x^71+419x^72+160x^73+314x^74+176x^75+162x^76+48x^77+50x^78+12x^79+30x^80+8x^82+4x^84+8x^86+2x^98

The gray image is a code over GF(2) with n=584, k=11 and d=280.
This code was found by Heurico 1.16 in 0.297 seconds.