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

generates a code of length 78 over Z4[X]/(X^3+2,2X) 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 0.516 seconds.