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

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

Homogenous weight enumerator: w(x)=1x^0+326x^72+128x^74+160x^76+128x^78+254x^80+26x^88+1x^128

The gray image is a code over GF(2) with n=304, k=10 and d=144.
This code was found by Heurico 1.16 in 99.2 seconds.