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

generates a code of length 78 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+29x^74+67x^76+64x^77+711x^78+64x^79+54x^80+27x^82+5x^84+1x^86+1x^152

The gray image is a code over GF(2) with n=624, k=10 and d=296.
This code was found by Heurico 1.16 in 0.515 seconds.