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

generates a code of length 74 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+108x^70+108x^71+207x^72+632x^73+264x^74+312x^75+213x^76+32x^77+52x^78+36x^79+30x^80+24x^81+16x^82+8x^83+4x^84+1x^140

The gray image is a code over GF(2) with n=592, k=11 and d=280.
This code was found by Heurico 1.16 in 3.8 seconds.