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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+167x^62+4x^63+359x^64+52x^65+581x^66+160x^67+754x^68+344x^69+833x^70+448x^71+970x^72+472x^73+778x^74+368x^75+611x^76+152x^77+498x^78+44x^79+291x^80+4x^81+170x^82+68x^84+42x^86+15x^88+3x^90+2x^92+1x^100

The gray image is a code over GF(2) with n=288, k=13 and d=124.
This code was found by Heurico 1.16 in 6.45 seconds.