The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X+2  X
 0  2  0  0  0 2X+2  2 2X+2  0  0  0  0 2X+2  2 2X+2  2  0  0  0  0 2X+2  2 2X+2 2X+2  2 2X+2  2 2X  2  0  0 2X 2X 2X 2X  2 2X+2 2X 2X  2 2X+2 2X 2X  2 2X+2 2X  2 2X 2X+2 2X  0 2X+2 2X+2 2X 2X+2 2X  2 2X 2X 2X  0  2 2X+2  2  2  0 2X  0  0 2X+2  2 2X+2  2
 0  0  2  0 2X+2 2X+2  2  0  0  0 2X+2  2 2X+2  2  0  0 2X 2X  2 2X+2  2 2X+2 2X 2X 2X  2 2X+2  0 2X 2X 2X  2 2X+2  2 2X+2 2X 2X 2X 2X  2 2X+2 2X+2  2  0  0  0 2X+2 2X 2X+2  2  2 2X  0  0  2 2X  2  0  0 2X+2 2X+2 2X+2  2  0 2X  0 2X 2X+2  2  0  2  0 2X+2
 0  0  0  2 2X+2  0  2 2X+2 2X 2X+2  2 2X 2X 2X+2  2 2X 2X 2X+2  2 2X 2X 2X+2  2  0 2X  0  2 2X+2 2X+2  0  2 2X+2  0  2 2X  2 2X  0  2  0  2  2 2X  2 2X 2X  0 2X+2 2X+2  0 2X+2 2X+2  0  2 2X+2 2X 2X  0 2X+2 2X+2  0 2X  2 2X+2  0  0  2 2X+2  0 2X+2 2X  2 2X+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+46x^70+24x^71+281x^72+336x^73+260x^74+24x^75+45x^76+6x^78+1x^140

The gray image is a code over GF(2) with n=584, k=10 and d=280.
This code was found by Heurico 1.16 in 23 seconds.