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

generates a code of length 75 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+134x^70+20x^71+69x^72+260x^73+352x^74+472x^75+282x^76+248x^77+92x^78+20x^79+23x^80+4x^81+48x^82+6x^84+14x^86+2x^88+1x^136

The gray image is a code over GF(2) with n=600, k=11 and d=280.
This code was found by Heurico 1.16 in 126 seconds.