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  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  1  1  1  X  1  X  1  1  2  1  1  X  X  0  0 2X+2 2X+2
 0  X  0  X 2X  0 3X  X 2X+2 3X+2 2X+2 3X+2  2 X+2 2X+2 3X+2  0 2X 3X 3X  0 2X+2 3X 3X+2 2X+2 X+2 2X 3X+2  2 3X+2  2  X  0 2X+2  X  X  2 3X 2X 3X 2X+2 3X  2  2 3X+2  0 X+2 X+2 X+2 2X+2 X+2 3X+2 2X+2 2X 2X 3X+2  X 2X+2  0 3X+2  X 3X 3X+2  2 2X  X X+2  X 2X+2  0  0  0  2 2X+2
 0  0  X  X 2X+2 3X+2 3X+2 2X+2 2X+2 X+2  X  2  0 3X 3X+2 2X  0 X+2 3X+2  2  2 3X+2 3X  2  2 X+2 3X 2X 2X 3X 3X  0 2X 3X 3X 2X 3X+2 2X+2  2 X+2  X 2X  2  2 X+2 3X 3X+2 2X 2X+2 2X 3X 2X+2 2X 3X+2 X+2  X  2 X+2 3X  0  2 2X+2 2X X+2 3X  0  0 2X+2 X+2 3X+2  X  X  X  X
 0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X  0  0  0 2X  0 2X 2X  0  0  0  0 2X  0  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+216x^70+48x^71+342x^72+336x^73+240x^74+336x^75+271x^76+48x^77+152x^78+24x^80+32x^82+1x^92+1x^128

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 0.469 seconds.