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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+54x^62+96x^64+128x^66+198x^68+294x^70+364x^72+934x^74+2080x^76+2048x^78+936x^80+356x^82+224x^84+162x^86+115x^88+78x^90+56x^92+30x^94+23x^96+8x^98+2x^100+4x^102+1x^120

The gray image is a code over GF(2) with n=308, k=13 and d=124.
This code was found by Heurico 1.16 in 9.24 seconds.