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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+26x^72+68x^76+320x^78+73x^80+20x^84+3x^88+1x^152

The gray image is a code over GF(2) with n=312, k=9 and d=144.
This code was found by Heurico 1.16 in 0.266 seconds.