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  X  1  1  X  1  1  X  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  1  1  1  X  X  2  0  X  X  X  1
 0 2X+2  0  2  0  0  2 2X+2  0  0  2 2X+2  0  0  2 2X+2  0  2  0 2X+2  0  2  0 2X+2 2X  0  0 2X  2 2X+2 2X  0 2X  2  0 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+2 2X  2 2X 2X 2X+2  2  2 2X+2 2X  0 2X+2  2  0  0
 0  0 2X+2  2  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2  0 2X 2X+2  2 2X 2X 2X+2  2 2X  2 2X  2  2 2X+2 2X  2 2X 2X+2 2X+2  2 2X 2X 2X+2  2 2X 2X  2  2  0 2X 2X+2  2 2X 2X  2  2  0  0 2X+2 2X+2 2X  0  2 2X+2  0  0 2X+2 2X+2 2X  0 2X+2  2  0  2  0  2  2 2X+2  0 2X+2  0
 0  0  0 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X  0 2X  0  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X 2X 2X  0 2X 2X  0 2X  0  0  0  0 2X  0  0  0  0 2X 2X  0  0  0
 0  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X  0  0  0  0  0 2X 2X 2X 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0 2X  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0 2X  0  0  0 2X 2X  0  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+8x^72+72x^73+88x^74+316x^75+62x^76+312x^77+84x^78+64x^79+7x^80+3x^82+4x^83+2x^84+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 0.468 seconds.