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

generates a code of length 75 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+128x^71+122x^72+160x^73+679x^74+268x^75+240x^76+200x^77+72x^78+56x^79+21x^80+48x^81+16x^82+28x^83+8x^85+1x^138

The gray image is a code over GF(2) with n=600, k=11 and d=284.
This code was found by Heurico 1.16 in 39.3 seconds.