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

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+52x^66+125x^68+201x^70+64x^71+182x^72+128x^73+85x^74+64x^75+43x^76+27x^78+28x^80+19x^82+4x^84+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 13 seconds.