The generator matrix

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

generates a code of length 73 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+94x^69+265x^70+314x^71+251x^72+308x^73+242x^74+212x^75+189x^76+78x^77+69x^78+16x^79+5x^80+2x^95+1x^100+1x^104

The gray image is a code over GF(2) with n=584, k=11 and d=276.
This code was found by Heurico 1.16 in 0.438 seconds.