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

generates a code of length 76 over Z4[X]/(X^3+2,2X) 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.