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

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+322x^70+288x^71+476x^72+128x^73+736x^74+192x^75+736x^76+128x^77+476x^78+288x^79+322x^80+2x^86+1x^128

The gray image is a code over GF(2) with n=600, k=12 and d=280.
This code was found by Heurico 1.16 in 2.52 seconds.