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

generates a code of length 76 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+10x^69+37x^70+34x^71+89x^72+44x^73+121x^74+62x^75+1147x^76+300x^77+70x^78+14x^79+42x^80+12x^81+3x^82+18x^83+1x^84+18x^85+24x^86+1x^142

The gray image is a code over GF(2) with n=608, k=11 and d=276.
This code was found by Heurico 1.16 in 5.01 seconds.