The generator matrix

 1  0  0  1  1  1  2  2 2X+2  1  1  2  1  1 3X  1  1 3X  X  1  1  1 X+2 3X+2  1  1 3X+2  1  1  2  1 2X  1 2X 3X+2  1 2X+2  1  1  1 3X  1  1  1 3X+2  1  1  1 2X+2  0 X+2  1  1  0  1  1  1 3X X+2  1  X 2X 3X+2  1  1 2X 2X  1 X+2  1 X+2  1  1  1  1
 0  1  0  0  3  3  1  X  1 2X 2X+3  1  2  1 3X+2 3X 3X+3  1  1 3X+3 3X+2 3X+1  1 2X+2 X+1 X+2  1  X  2 2X 3X+3 3X  1  1  1 2X  1 3X+3 3X+2 X+3  1  X 2X+1 3X 3X+2  3 X+1 2X  1  1  1  3  2  1 2X+2 2X+2 X+2 2X 3X 2X+3  1 3X+2 3X+2 3X+3  3  2 2X+2  2  1 X+3 2X  0  X  0  0
 0  0  1 X+1 3X+1 2X 3X+3  1 3X  X 3X  3  3 2X+3  1  1  2  3 3X 2X+1  X 3X+1  0  1  2 X+1 3X+3  0  1  1 X+3  1 2X+2 2X  3 3X+3 X+2 X+2 X+2  X  0 2X+3 3X+2 X+3  1 2X+1  3 2X X+1 X+3 X+2  3  X X+2  1 X+3 2X+1  1  1 3X+3 2X+2  1  1 2X+3 3X  1  1 X+2 X+3  X  1  3  2 X+2  0
 0  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0  0 2X  0  0 2X 2X  0 2X  0 2X  0  0  0  0  0  0  0 2X  0 2X 2X 2X  0 2X  0  0 2X  0  0 2X 2X 2X  0 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+144x^70+630x^71+1046x^72+1194x^73+1058x^74+992x^75+741x^76+676x^77+540x^78+516x^79+286x^80+142x^81+103x^82+52x^83+36x^84+20x^85+10x^86+2x^87+1x^88+1x^90+1x^92

The gray image is a code over GF(2) with n=600, k=13 and d=280.
This code was found by Heurico 1.16 in 0.969 seconds.