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

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

Homogenous weight enumerator: w(x)=1x^0+36x^70+62x^71+218x^72+248x^73+347x^74+368x^75+348x^76+168x^77+60x^78+18x^79+113x^80+28x^81+16x^82+8x^84+4x^85+4x^86+1x^138

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 0.672 seconds.