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

generates a code of length 76 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+23x^70+74x^71+52x^72+64x^73+194x^74+386x^75+531x^76+374x^77+142x^78+88x^79+39x^80+4x^81+18x^82+18x^83+16x^84+6x^85+7x^86+10x^87+1x^140

The gray image is a code over GF(2) with n=608, k=11 and d=280.
This code was found by Heurico 1.16 in 0.562 seconds.