The generator matrix

 1  0  1  1  1 X+2  1  1  0  1 X+2  1  1  1  0  1  1 X+2  1  0  1  1 X+2  1  1  1  1  X  1  2  1  1  1  1 X+2  0  1  1  1  1  1  X  X  1  0  1  1  1  1  1  1  1 X+2  1  1 X+2  1  1  1 X+2  1  X  1  1  1  1  1  1  2  1  1  1
 0  1 X+1 X+2  1  1  0 X+1  1  3  1 X+2  0 X+1  1  3 X+2  1  X  1 X+1  3  1  0  0 X+2 X+3  1  0  1  3 X+2  3  2  1  1 X+1 X+2  3  2  0  1  1 X+2  1 X+3  1  3 X+1 X+2  2  2  1  X X+1  1 X+3  1  3  1  X X+2 X+1  3 X+3  3 X+1 X+1  2 X+3  1 X+2
 0  0  2  0  0  0  0  0  2  2  2  0  0  0  0  2  2  0  2  2  0  2  2  2  2  0  2  2  0  2  2  2  0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  2  2  0  2  0  0  0  2  0  0  0  0  2  0  2  2  0  2  2  2  0  0  2  0  0
 0  0  0  2  0  0  0  0  0  2  2  0  2  2  2  0  2  2  0  2  2  2  0  2  0  0  0  2  0  2  0  2  2  2  0  2  2  2  0  0  0  2  0  2  0  0  0  0  2  0  0  2  0  0  2  0  2  0  2  0  2  2  0  0  2  2  2  0  0  2  0  0
 0  0  0  0  2  0  0  2  2  2  0  2  0  2  0  2  0  0  2  2  2  0  0  2  0  0  0  0  0  2  2  2  2  0  0  0  2  0  2  0  2  0  0  0  2  2  0  2  0  2  2  0  0  0  2  2  0  2  0  2  2  0  0  0  2  0  0  2  2  2  0  2
 0  0  0  0  0  2  0  2  0  2  2  0  0  0  2  2  2  0  2  0  2  0  2  2  2  2  2  0  2  2  0  0  0  2  0  2  2  0  2  0  0  0  0  2  2  0  2  2  2  2  0  0  0  0  0  0  2  2  2  0  0  2  0  2  0  2  0  0  2  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  2  0  2  2  2  2  0  0  2  0  2  2  0  2  0  0  0  0  2  2  2  0  2  0  0  0  2  2  2  0  0  0  0  0  2  2  2  0  2  2  2  2  2  2  0  2  2  0  0  0  0

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+54x^65+107x^66+102x^67+207x^68+96x^69+245x^70+156x^71+217x^72+120x^73+196x^74+76x^75+189x^76+104x^77+84x^78+44x^79+22x^80+10x^81+4x^82+6x^83+2x^86+1x^88+1x^90+1x^94+2x^96+1x^104

The gray image is a code over GF(2) with n=288, k=11 and d=130.
This code was found by Heurico 1.16 in 1.09 seconds.