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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+40x^73+34x^74+40x^75+61x^76+170x^77+54x^78+282x^79+40x^80+156x^81+20x^82+44x^83+19x^84+18x^85+14x^86+18x^87+6x^88+6x^90+1x^152

The gray image is a code over GF(2) with n=316, k=10 and d=146.
This code was found by Heurico 1.16 in 0.442 seconds.