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

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

Homogenous weight enumerator: w(x)=1x^0+152x^70+80x^71+322x^72+352x^73+260x^74+592x^75+63x^76+120x^78+93x^80+12x^82+1x^140

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 82.4 seconds.