This paper deals with the problem of massive random access for Gaussian multiple access channel (MAC). We continue to investigate the coding scheme for Gaussian MAC proposed by A. Vem et al. in 2017. The proposed scheme consists of four parts: (i) the data transmission is partitioned into time slots; (ii) the data, transmitted in each slot, is split into two parts, the first one set an interleaver of the low-density parity-check (LDPC) type code and is encoded by spreading sequence or codewords that are designed to be decoded by compressed sensing type decoding; (iii) the another part of transmitted data is encoded by LDPC type code and decoded using a joint message passing decoding algorithm designed for the T-user binary input Gaussian MAC; (iv) users repeat their codeword in multiple slots. In this paper we are concentrated on the third part of considered scheme. We generalized the PEXIT charts to optimize the protograph of LDPC code for Gaussian MAC. The simulation results, obtained at the end of the paper, were analyzed and compared with obtained theoretical bounds and thresholds. Obtained simulation results shows that proposed LDPC code constructions have better performance under joint decoding algorithm over Gaussian MAC than LDPC codes considered by A. Vem et al. in 2017, that leads to the better performance of overall transmission system.