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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+60x^66+103x^68+16x^69+147x^70+112x^71+187x^72+112x^73+128x^74+16x^75+58x^76+48x^78+31x^80+3x^84+1x^86+1x^136

The gray image is a code over GF(2) with n=288, k=10 and d=132.
This code was found by Heurico 1.16 in 0.317 seconds.