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

generates a code of length 76 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+21x^72+72x^73+43x^74+212x^75+294x^76+278x^77+18x^78+60x^79+4x^80+16x^81+2x^82+2x^85+1x^130

The gray image is a code over GF(2) with n=608, k=10 and d=288.
This code was found by Heurico 1.16 in 0.359 seconds.