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  1  1  1  1  1  1  1  1  1  X  2  X  X  X  X
 0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0  2  2 2X 2X  2 2X  2 2X 2X+2 2X  2 2X  2 2X  2  0 2X+2 2X  2 2X  2 2X  2  0  2 2X 2X+2 2X  2 2X  2  0 2X+2 2X  2 2X  2 2X  2  0 2X+2  0 2X+2 2X+2 2X+2 2X+2 2X+2  0  0
 0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0 2X 2X 2X  0
 0  0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0 2X  0 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X  0  0 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X  0 2X
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0  0 2X  0 2X 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X 2X
 0  0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X  0 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X  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+25x^70+16x^71+63x^72+240x^73+335x^74+240x^75+60x^76+16x^77+23x^78+3x^80+1x^82+1x^136

The gray image is a code over GF(2) with n=592, k=10 and d=280.
This code was found by Heurico 1.16 in 0.422 seconds.